document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116587>Question 116587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the quadratic formula to solve the equation.\r<BR>\n" );
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document.write( "2x^2+12x= -5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84755 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=84755\">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%2B12x=-5 ALIGN=MIDDLE  ALT=\"2x%5E2%2B12x=-5\"   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%2B12x%2B5=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B12x%2B5=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( "<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" );
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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%2B12%2Ax%2B5=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B12%2Ax%2B5=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=12 ALIGN=MIDDLE  ALT=\"b=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5 ALIGN=MIDDLE  ALT=\"c=5\"   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+=+%28-12+%2B-+sqrt%28+%2812%29%5E2-4%2A2%2A5+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+%2812%29%5E2-4%2A2%2A5+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=12, and c=5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12+%2B-+sqrt%28+144-4%2A2%2A5+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+144-4%2A2%2A5+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 12 to get 144  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12+%2B-+sqrt%28+144%2B-40+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+144%2B-40+%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%2A5%2A2 ALIGN=MIDDLE  ALT=\"-4%2A5%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40 ALIGN=MIDDLE  ALT=\"-40\"   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+=+%28-12+%2B-+sqrt%28+104+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+104+%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+=+%28-12+%2B-+2%2Asqrt%2826%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+2%2Asqrt%2826%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+=+%28-12+%2B-+2%2Asqrt%2826%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+2%2Asqrt%2826%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+=+%28-12+%2B+2%2Asqrt%2826%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B+2%2Asqrt%2826%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12+-+2%2Asqrt%2826%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-12+-+2%2Asqrt%2826%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=-12%2F4%2B2%2Asqrt%2826%29%2F4 ALIGN=MIDDLE  ALT=\"x=-12%2F4%2B2%2Asqrt%2826%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-12%2F4-2%2Asqrt%2826%29%2F4 ALIGN=MIDDLE  ALT=\"x=-12%2F4-2%2Asqrt%2826%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=-3%2Bsqrt%2826%29%2F2 ALIGN=MIDDLE  ALT=\"x=-3%2Bsqrt%2826%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3-sqrt%2826%29%2F2 ALIGN=MIDDLE  ALT=\"x=-3-sqrt%2826%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=-0.450490243203608 ALIGN=MIDDLE  ALT=\"x=-0.450490243203608\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5.54950975679639 ALIGN=MIDDLE  ALT=\"x=-5.54950975679639\"   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=-0.450490243203608 ALIGN=MIDDLE  ALT=\"x=-0.450490243203608\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5.54950975679639 ALIGN=MIDDLE  ALT=\"x=-5.54950975679639\"   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%2B12%2Ax%2B5 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B12%2Ax%2B5\"   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+-15.5495097567964%2C+9.54950975679639%2C+-15.5495097567964%2C+9.54950975679639%2C2%2Ax%5E2%2B12%2Ax%2B5%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=-0.450490243203608 ALIGN=MIDDLE  ALT=\"x=-0.450490243203608\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5.54950975679639 ALIGN=MIDDLE  ALT=\"x=-5.54950975679639\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer<BR>\n" );
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