document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201194>Question 201194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the quadratic formula to solve the equation. Give both exact and approximate answers.\r<BR>\n" );
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document.write( "3m2 + 12m + 5 = 0<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 #151410 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=151410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m%5E2%2B12m%2B5=0 ALIGN=MIDDLE  ALT=\"3m%5E2%2B12m%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m%5E2%2B12m%2B5 ALIGN=MIDDLE  ALT=\"3m%5E2%2B12m%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Am%5E2%2BBm%2BC ALIGN=MIDDLE  ALT=\"Am%5E2%2BBm%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3 ALIGN=MIDDLE  ALT=\"A=3\"   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( "Let's use the quadratic formula to solve for \"m\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"m+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%283%29%285%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"m+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%283%29%285%29+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3 ALIGN=MIDDLE  ALT=\"A=3\"   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=m+=+%28-12+%2B-+sqrt%28+144-4%283%29%285%29+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"m+=+%28-12+%2B-+sqrt%28+144-4%283%29%285%29+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   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=m+=+%28-12+%2B-+sqrt%28+144-60+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"m+=+%28-12+%2B-+sqrt%28+144-60+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%283%29%285%29 ALIGN=MIDDLE  ALT=\"4%283%29%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   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=m+=+%28-12+%2B-+sqrt%28+84+%29%29%2F%282%283%29%29 ALIGN=MIDDLE  ALT=\"m+=+%28-12+%2B-+sqrt%28+84+%29%29%2F%282%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60 ALIGN=MIDDLE  ALT=\"60\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   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=m+=+%28-12+%2B-+sqrt%28+84+%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"m+=+%28-12+%2B-+sqrt%28+84+%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   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=m+=+%28-12+%2B-+2%2Asqrt%2821%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"m+=+%28-12+%2B-+2%2Asqrt%2821%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, 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=m+=+%28-12%2B2%2Asqrt%2821%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"m+=+%28-12%2B2%2Asqrt%2821%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-12-2%2Asqrt%2821%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"m+=+%28-12-2%2Asqrt%2821%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-6%2Bsqrt%2821%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"m+=+%28-6%2Bsqrt%2821%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-6-sqrt%2821%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"m+=+%28-6-sqrt%2821%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-6%2Bsqrt%2821%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"m+=+%28-6%2Bsqrt%2821%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-6-sqrt%2821%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"m+=+%28-6-sqrt%2821%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-0.472 ALIGN=MIDDLE  ALT=\"m=-0.472\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-3.528 ALIGN=MIDDLE  ALT=\"m=-3.528\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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