document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115684>Question 115684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a test tomorrow and am having a lot of trouble with quadratic equations. i understand some things, but others do not make sense at all. below are 3 problems that i do not understand how to solve. if you could solve the problems and show the steps, that would really help me a lot.\r<BR>\n" );
document.write( "\n" );
document.write( "1. 3x^2 + 9 = 0<BR>\n" );
document.write( "2. 2x^2 - 14x - 10 = 0<BR>\n" );
document.write( "3. -2u^2 + 6 = 3u^2 - 10u\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i attempted problem one and the answer i ended up with was x = the square root of 3. i thought for those types of problems there were supposed to be two answers though, like x + sq. root three  and  x equals (another number) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84186 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1\r<BR>\n" );
document.write( "\n" );
document.write( "Well you're forgetting the other part of the answer which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You are correct, there should be two answers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "#2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's use the quadratic formula to solve for x:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Starting with the general quadratic\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2-14%2Ax-10=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-14%2Ax-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-14 ALIGN=MIDDLE  ALT=\"b=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-10 ALIGN=MIDDLE  ALT=\"c=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--14+%2B-+sqrt%28+%28-14%29%5E2-4%2A2%2A-10+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28--14+%2B-+sqrt%28+%28-14%29%5E2-4%2A2%2A-10+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=-14, and c=-10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%2A2%2A-10+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%2A2%2A-10+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -14 to get 14\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+%2B-+sqrt%28+196-4%2A2%2A-10+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B-+sqrt%28+196-4%2A2%2A-10+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -14 to get 196  (note: remember when you square -14, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-14%29%5E2=-14%2A-14=196 ALIGN=MIDDLE  ALT=\"%28-14%29%5E2=-14%2A-14=196\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+%2B-+sqrt%28+196%2B80+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B-+sqrt%28+196%2B80+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-10%2A2 ALIGN=MIDDLE  ALT=\"-4%2A-10%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80 ALIGN=MIDDLE  ALT=\"80\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+%2B-+sqrt%28+276+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B-+sqrt%28+276+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+%2B-+2%2Asqrt%2869%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B-+2%2Asqrt%2869%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+%2B-+2%2Asqrt%2869%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B-+2%2Asqrt%2869%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So now the expression breaks down into two parts\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+%2B+2%2Asqrt%2869%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%2814+%2B+2%2Asqrt%2869%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2814+-+2%2Asqrt%2869%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%2814+-+2%2Asqrt%2869%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now break up the fraction\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B14%2F4%2B2%2Asqrt%2869%29%2F4 ALIGN=MIDDLE  ALT=\"x=%2B14%2F4%2B2%2Asqrt%2869%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B14%2F4-2%2Asqrt%2869%29%2F4 ALIGN=MIDDLE  ALT=\"x=%2B14%2F4-2%2Asqrt%2869%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7+%2F+2%2Bsqrt%2869%29%2F2 ALIGN=MIDDLE  ALT=\"x=7+%2F+2%2Bsqrt%2869%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7+%2F+2-sqrt%2869%29%2F2 ALIGN=MIDDLE  ALT=\"x=7+%2F+2-sqrt%2869%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So these expressions approximate to\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.65331193145904 ALIGN=MIDDLE  ALT=\"x=7.65331193145904\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.653311931459037 ALIGN=MIDDLE  ALT=\"x=-0.653311931459037\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our solutions are:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.65331193145904 ALIGN=MIDDLE  ALT=\"x=7.65331193145904\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.653311931459037 ALIGN=MIDDLE  ALT=\"x=-0.653311931459037\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2-14%2Ax-10 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-14%2Ax-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10.653311931459%2C+17.653311931459%2C+-10.653311931459%2C+17.653311931459%2C2%2Ax%5E2%2B-14%2Ax%2B-10%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when we use the root finder feature on a calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.65331193145904 ALIGN=MIDDLE  ALT=\"x=7.65331193145904\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.653311931459037 ALIGN=MIDDLE  ALT=\"x=-0.653311931459037\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2u%5E2%2B6=3u%5E2-10u ALIGN=MIDDLE  ALT=\"-2u%5E2%2B6=3u%5E2-10u\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2u%5E2%2B6-3u%5E2%2B10u=0 ALIGN=MIDDLE  ALT=\"-2u%5E2%2B6-3u%5E2%2B10u=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move all of the terms to the left side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2u%5E2-3u%5E2%2B10u%2B6=0 ALIGN=MIDDLE  ALT=\"-2u%5E2-3u%5E2%2B10u%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Sort the terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5u%5E2%2B10u%2B6=0 ALIGN=MIDDLE  ALT=\"-5u%5E2%2B10u%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's use the quadratic formula to solve for u:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Starting with the general quadratic\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=au%5E2%2Bbu%2Bc=0 ALIGN=MIDDLE  ALT=\"au%5E2%2Bbu%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2Au%5E2%2B10%2Au%2B6=0 ALIGN=MIDDLE  ALT=\"-5%2Au%5E2%2B10%2Au%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-5 ALIGN=MIDDLE  ALT=\"a=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=10 ALIGN=MIDDLE  ALT=\"b=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6 ALIGN=MIDDLE  ALT=\"c=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A-5%2A6+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"u+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A-5%2A6+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-5, b=10, and c=6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-10+%2B-+sqrt%28+100-4%2A-5%2A6+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"u+=+%28-10+%2B-+sqrt%28+100-4%2A-5%2A6+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 10 to get 100  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-10+%2B-+sqrt%28+100%2B120+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"u+=+%28-10+%2B-+sqrt%28+100%2B120+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A6%2A-5 ALIGN=MIDDLE  ALT=\"-4%2A6%2A-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120 ALIGN=MIDDLE  ALT=\"120\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-10+%2B-+sqrt%28+220+%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"u+=+%28-10+%2B-+sqrt%28+220+%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-10+%2B-+2%2Asqrt%2855%29%29%2F%282%2A-5%29 ALIGN=MIDDLE  ALT=\"u+=+%28-10+%2B-+2%2Asqrt%2855%29%29%2F%282%2A-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-10+%2B-+2%2Asqrt%2855%29%29%2F-10 ALIGN=MIDDLE  ALT=\"u+=+%28-10+%2B-+2%2Asqrt%2855%29%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -5 to get -10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So now the expression breaks down into two parts\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-10+%2B+2%2Asqrt%2855%29%29%2F-10 ALIGN=MIDDLE  ALT=\"u+=+%28-10+%2B+2%2Asqrt%2855%29%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-10+-+2%2Asqrt%2855%29%29%2F-10 ALIGN=MIDDLE  ALT=\"u+=+%28-10+-+2%2Asqrt%2855%29%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now break up the fraction\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-10%2F-10%2B2%2Asqrt%2855%29%2F-10 ALIGN=MIDDLE  ALT=\"u=-10%2F-10%2B2%2Asqrt%2855%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-10%2F-10-2%2Asqrt%2855%29%2F-10 ALIGN=MIDDLE  ALT=\"u=-10%2F-10-2%2Asqrt%2855%29%2F-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=1-sqrt%2855%29%2F5 ALIGN=MIDDLE  ALT=\"u=1-sqrt%2855%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=1%2Bsqrt%2855%29%2F5 ALIGN=MIDDLE  ALT=\"u=1%2Bsqrt%2855%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So these expressions approximate to\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-0.483239697419133 ALIGN=MIDDLE  ALT=\"u=-0.483239697419133\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=2.48323969741913 ALIGN=MIDDLE  ALT=\"u=2.48323969741913\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our solutions are:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=-0.483239697419133 ALIGN=MIDDLE  ALT=\"u=-0.483239697419133\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=2.48323969741913 ALIGN=MIDDLE  ALT=\"u=2.48323969741913\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2Ax%5E2%2B10%2Ax%2B6 ALIGN=MIDDLE  ALT=\"-5%2Ax%5E2%2B10%2Ax%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace u with x), we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10.4832396974191%2C+12.4832396974191%2C+-10.4832396974191%2C+12.4832396974191%2C-5%2Ax%5E2%2B10%2Ax%2B6%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when we use the root finder feature on a calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.483239697419133 ALIGN=MIDDLE  ALT=\"x=-0.483239697419133\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.48323969741913 ALIGN=MIDDLE  ALT=\"x=2.48323969741913\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );