document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142982>Question 142982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the following, solve.  Find exact solutions\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104029 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=104029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4-3y%5E2=-1 ALIGN=MIDDLE  ALT=\"y%5E4-3y%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4-3y%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"y%5E4-3y%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1 to both sides\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=y%5E4 ALIGN=MIDDLE  ALT=\"x%5E2=y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4 ALIGN=MIDDLE  ALT=\"y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3%2Ax%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2-3%2Ax%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3 ALIGN=MIDDLE  ALT=\"b=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=1 ALIGN=MIDDLE  ALT=\"c=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-3, and c=1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -3 to get 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%28+9-4%2A1%2A1+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+9-4%2A1%2A1+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -3 to get 9  (note: remember when you square -3, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2=-3%2A-3=9 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2=-3%2A-3=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%28+9%2B-4+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+9%2B-4+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A1%2A1 ALIGN=MIDDLE  ALT=\"-4%2A1%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%28+5+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+5+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%285%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%285%29%29%2F%282%2A1%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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+-+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%283+-+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the solutions in terms of x are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%283+%2B+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+-+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%283+-+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But remember, we let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this means \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+%283+%2B+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"y%5E2+=+%283+%2B+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+%283+-+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"y%5E2+=+%283+-+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the square root of both sides in each case\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=0%2B-sqrt%28+%283+%2B+sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"y+=0%2B-sqrt%28+%283+%2B+sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=0%2B-sqrt%28+%283+-+sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"y+=0%2B-sqrt%28+%283+-+sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So after breaking up the expressions, we get the four solutions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28+%283+%2B+sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28+%283+%2B+sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%28+%283+%2B+sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%28+%283+%2B+sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=sqrt%28+%283+-+sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"y+=sqrt%28+%283+-+sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=-sqrt%28+%283+-+sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"y+=-sqrt%28+%283+-+sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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