document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87266>Question 87266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following using the square  root method or the quadratic equation.<BR>\n" );
document.write( "66x^2 -31x -9 + 0<BR>\n" );
document.write( "Not understanding this can you help Please!!<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63200 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=63200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Starting with the general quadratic\r<BR>\n" );
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document.write( "the general form of the quadratic equation is:\r<BR>\n" );
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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" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66%2Ax%5E2-31%2Ax-9=0 ALIGN=MIDDLE  ALT=\"66%2Ax%5E2-31%2Ax-9=0\"   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+=+%2831+%2B-+sqrt%28+%28-31%29%5E2-4%2A66%2A-9+%29%29%2F%282%2A66%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+%28-31%29%5E2-4%2A66%2A-9+%29%29%2F%282%2A66%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=66, b=-31, and c=-9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+sqrt%28+961-4%2A66%2A-9+%29%29%2F%282%2A66%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+961-4%2A66%2A-9+%29%29%2F%282%2A66%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -31 to get 961\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+sqrt%28+961%2B2376+%29%29%2F%282%2A66%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+961%2B2376+%29%29%2F%282%2A66%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-9%2A66 ALIGN=MIDDLE  ALT=\"-4%2A-9%2A66\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2376 ALIGN=MIDDLE  ALT=\"2376\"   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+=+%2831+%2B-+sqrt%28+3337+%29%29%2F%282%2A66%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+3337+%29%29%2F%282%2A66%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+=+%2831+%2B-+sqrt%283337%29%29%2F%282%2A66%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%283337%29%29%2F%282%2A66%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify 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+=+%2831+%2B-+sqrt%283337%29%29%2F132 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%283337%29%29%2F132\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 66 to get 132\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+=+%2831+%2B+sqrt%283337%29%29%2F132 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B+sqrt%283337%29%29%2F132\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+-+sqrt%283337%29%29%2F132 ALIGN=MIDDLE  ALT=\"x+=+%2831+-+sqrt%283337%29%29%2F132\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.672475548910187 ALIGN=MIDDLE  ALT=\"x=0.672475548910187\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.202778579213218 ALIGN=MIDDLE  ALT=\"x=-0.202778579213218\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.672475548910187 ALIGN=MIDDLE  ALT=\"x=0.672475548910187\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.202778579213218 ALIGN=MIDDLE  ALT=\"x=-0.202778579213218\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=66%2Ax%5E2-31%2Ax-9 ALIGN=MIDDLE  ALT=\"66%2Ax%5E2-31%2Ax-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10.2027785792132%2C+10.6724755489102%2C+-10.2027785792132%2C+10.6724755489102%2C66%2Ax%5E2%2B-31%2Ax%2B-9%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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=0.672475548910187 ALIGN=MIDDLE  ALT=\"x=0.672475548910187\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.202778579213218 ALIGN=MIDDLE  ALT=\"x=-0.202778579213218\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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