document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=841172>Question 841172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the lengths of each side of the right triangle <BR>\n" );
document.write( "short leg is 2x+1<BR>\n" );
document.write( "long leg is 11x+5<BR>\n" );
document.write( "hypotenuse is 12x+1<BR>\n" );
document.write( "I know that first you're suppose to write the problem out like this<BR>\n" );
document.write( "(12x+1)^2=(2x+1)^2+(11x+5)^2<BR>\n" );
document.write( "but after this I got lost<BR>\n" );
document.write( "please help and break it down as much as possible <BR>\n" );
document.write( "please and thank you :D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #506680 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=506680\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So far so good. Now we just need to solve for x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x%2B1%29%5E2=%282x%2B1%29%5E2%2B%2811x%2B5%29%5E2 ALIGN=MIDDLE  ALT=\"%2812x%2B1%29%5E2=%282x%2B1%29%5E2%2B%2811x%2B5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x%2B1%29%2812x%2B1%29=%282x%2B1%29%282x%2B1%29%2B%2811x%2B5%29%2811x%2B5%29 ALIGN=MIDDLE  ALT=\"%2812x%2B1%29%2812x%2B1%29=%282x%2B1%29%282x%2B1%29%2B%2811x%2B5%29%2811x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2812x%2B1%29%2B1%2812x%2B1%29=2x%282x%2B1%29%2B1%282x%2B1%29%2B11x%2811x%2B5%29%2B5%2811x%2B5%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144x%5E2%2B12x%2B12x%2B1=4x%5E2%2B2x%2B2x%2B1%2B121x%5E2%2B55x%2B55x%2B25 ALIGN=MIDDLE  ALT=\"144x%5E2%2B12x%2B12x%2B1=4x%5E2%2B2x%2B2x%2B1%2B121x%5E2%2B55x%2B55x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144x%5E2%2B24x%2B1=125x%5E2%2B114x%2B26 ALIGN=MIDDLE  ALT=\"144x%5E2%2B24x%2B1=125x%5E2%2B114x%2B26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144x%5E2%2B24x%2B1-125x%5E2-114x-26=0 ALIGN=MIDDLE  ALT=\"144x%5E2%2B24x%2B1-125x%5E2-114x-26=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19x%5E2-90x-25=0 ALIGN=MIDDLE  ALT=\"19x%5E2-90x-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now from here, you could factor, but I like using the quadratic formula (since it always works for any quadratic)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
document.write( "\n" );
document.write( "  <BR>\n" );
document.write( "  Starting with the general quadratic<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\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;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  the general solution using the quadratic equation is:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\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;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2Ax%5E2-90%2Ax-25=0 ALIGN=MIDDLE  ALT=\"19%2Ax%5E2-90%2Ax-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=19 ALIGN=MIDDLE  ALT=\"a=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-90 ALIGN=MIDDLE  ALT=\"b=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-25 ALIGN=MIDDLE  ALT=\"c=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--90+%2B-+sqrt%28+%28-90%29%5E2-4%2A19%2A-25+%29%29%2F%282%2A19%29 ALIGN=MIDDLE  ALT=\"x+=+%28--90+%2B-+sqrt%28+%28-90%29%5E2-4%2A19%2A-25+%29%29%2F%282%2A19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=19, b=-90, and c=-25<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2890+%2B-+sqrt%28+%28-90%29%5E2-4%2A19%2A-25+%29%29%2F%282%2A19%29 ALIGN=MIDDLE  ALT=\"x+=+%2890+%2B-+sqrt%28+%28-90%29%5E2-4%2A19%2A-25+%29%29%2F%282%2A19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -90 to get 90<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2890+%2B-+sqrt%28+8100-4%2A19%2A-25+%29%29%2F%282%2A19%29 ALIGN=MIDDLE  ALT=\"x+=+%2890+%2B-+sqrt%28+8100-4%2A19%2A-25+%29%29%2F%282%2A19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -90 to get 8100  (note: remember when you square -90, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-90%29%5E2=-90%2A-90=8100 ALIGN=MIDDLE  ALT=\"%28-90%29%5E2=-90%2A-90=8100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2890+%2B-+sqrt%28+8100%2B1900+%29%29%2F%282%2A19%29 ALIGN=MIDDLE  ALT=\"x+=+%2890+%2B-+sqrt%28+8100%2B1900+%29%29%2F%282%2A19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-25%2A19 ALIGN=MIDDLE  ALT=\"-4%2A-25%2A19\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1900 ALIGN=MIDDLE  ALT=\"1900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2890+%2B-+sqrt%28+10000+%29%29%2F%282%2A19%29 ALIGN=MIDDLE  ALT=\"x+=+%2890+%2B-+sqrt%28+10000+%29%29%2F%282%2A19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2890+%2B-+100%29%2F%282%2A19%29 ALIGN=MIDDLE  ALT=\"x+=+%2890+%2B-+100%29%2F%282%2A19%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>)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2890+%2B-+100%29%2F38 ALIGN=MIDDLE  ALT=\"x+=+%2890+%2B-+100%29%2F38\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 19 to get 38<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So now the expression breaks down into two parts<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2890+%2B+100%29%2F38 ALIGN=MIDDLE  ALT=\"x+=+%2890+%2B+100%29%2F38\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2890+-+100%29%2F38 ALIGN=MIDDLE  ALT=\"x+=+%2890+-+100%29%2F38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Lets look at the first part:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2890+%2B+100%29%2F38 ALIGN=MIDDLE  ALT=\"x=%2890+%2B+100%29%2F38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=190%2F38 ALIGN=MIDDLE  ALT=\"x=190%2F38\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So one answer is<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now lets look at the second part:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2890+-+100%29%2F38 ALIGN=MIDDLE  ALT=\"x=%2890+-+100%29%2F38\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-10%2F38 ALIGN=MIDDLE  ALT=\"x=-10%2F38\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F19 ALIGN=MIDDLE  ALT=\"x=-5%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So another answer is<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F19 ALIGN=MIDDLE  ALT=\"x=-5%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So our solutions are:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F19 ALIGN=MIDDLE  ALT=\"x=-5%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now because the hypotenuse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B1 ALIGN=MIDDLE  ALT=\"12x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-5%2F19 ALIGN=MIDDLE  ALT=\"x+=+-5%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" > the hypotenuse will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B1+=+12%28-5%2F19%29%2B1=-2.1578947368421 ALIGN=MIDDLE  ALT=\"12x%2B1+=+12%28-5%2F19%29%2B1=-2.1578947368421\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But we can't have a negative length. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-5%2F19 ALIGN=MIDDLE  ALT=\"x+=+-5%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be allowed as a solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the only solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > into each expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Short Leg: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+1+=+2%2A5%2B1+=+11 ALIGN=MIDDLE  ALT=\"2x+%2B+1+=+2%2A5%2B1+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Long Leg: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x+%2B+5+=+11%2A5%2B5+=+60 ALIGN=MIDDLE  ALT=\"11x+%2B+5+=+11%2A5%2B5+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hypotenuse: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x+%2B+1+=+12%2A5%2B1+=+61 ALIGN=MIDDLE  ALT=\"12x+%2B+1+=+12%2A5%2B1+=+61\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "=========================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Summary:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Short Leg: <font color=\"red\">11 units</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Long Leg: <font color=\"red\">60 units</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hypotenuse: <font color=\"red\">61 units</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );