document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116121>Question 116121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x squared + 10x = -1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84443 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=84443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B10x=-1 ALIGN=MIDDLE  ALT=\"2x%5E2%2B10x=-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=2x%5E2%2B10x%2B1=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B10x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move all of the terms to the left side\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( "<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=2%2Ax%5E2%2B10%2Ax%2B1=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B10%2Ax%2B1=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=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=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+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A2%2A1+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=10, 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+=+%28-10+%2B-+sqrt%28+100-4%2A2%2A1+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+100-4%2A2%2A1+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 10 to get 100  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B-+sqrt%28+100%2B-8+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+100%2B-8+%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%2A1%2A2 ALIGN=MIDDLE  ALT=\"-4%2A1%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   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+=+%28-10+%2B-+sqrt%28+92+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+92+%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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B-+2%2Asqrt%2823%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+2%2Asqrt%2823%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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B-+2%2Asqrt%2823%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+2%2Asqrt%2823%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\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+=+%28-10+%2B+2%2Asqrt%2823%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B+2%2Asqrt%2823%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+-+2%2Asqrt%2823%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-10+-+2%2Asqrt%2823%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-10%2F4%2B2%2Asqrt%2823%29%2F4 ALIGN=MIDDLE  ALT=\"x=-10%2F4%2B2%2Asqrt%2823%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-10%2F4-2%2Asqrt%2823%29%2F4 ALIGN=MIDDLE  ALT=\"x=-10%2F4-2%2Asqrt%2823%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5+%2F+2%2Bsqrt%2823%29%2F2 ALIGN=MIDDLE  ALT=\"x=-5+%2F+2%2Bsqrt%2823%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5+%2F+2-sqrt%2823%29%2F2 ALIGN=MIDDLE  ALT=\"x=-5+%2F+2-sqrt%2823%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.10208423834364 ALIGN=MIDDLE  ALT=\"x=-0.10208423834364\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4.89791576165636 ALIGN=MIDDLE  ALT=\"x=-4.89791576165636\"   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=-0.10208423834364 ALIGN=MIDDLE  ALT=\"x=-0.10208423834364\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4.89791576165636 ALIGN=MIDDLE  ALT=\"x=-4.89791576165636\"   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=2%2Ax%5E2%2B10%2Ax%2B1 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B10%2Ax%2B1\"   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+-14.8979157616564%2C+9.89791576165636%2C+-14.8979157616564%2C+9.89791576165636%2C2%2Ax%5E2%2B10%2Ax%2B1%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=-0.10208423834364 ALIGN=MIDDLE  ALT=\"x=-0.10208423834364\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4.89791576165636 ALIGN=MIDDLE  ALT=\"x=-4.89791576165636\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer<BR>\n" );
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