document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73777>Question 73777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2m^2+10m+6=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52753 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2+%2B+10m+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"2m%5E2+%2B+10m+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that every term on the left side of this equation has a common factor of 2. Therefore,<BR>\n" );
document.write( "we can simplify the equation by dividing both sides (all terms) by 2 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2+%2B+5m+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"m%5E2+%2B+5m+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can try to factor this, but it doesn't factor nicely. So let's go directly to the quadratic<BR>\n" );
document.write( "formula method.  This method says that if you have a quadratic equation of the form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "the solutions for x can be written directly as:<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%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B+sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+-+sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+-+sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that by comparing the simplified form of the quadratic equation you were given to <BR>\n" );
document.write( "this quadratic formula form, term by term, you know the answers can be directly <BR>\n" );
document.write( "figured by <BR>\n" );
document.write( "replacing x by m, a by 1, b by +5, and c by +3 in the solution forms.<BR>\n" );
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document.write( "With the appropriate substitutions the solution form:<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%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B+sqrt%28b%5E2+-+4%2Aa%2Ac%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-5+%2B+sqrt%285%5E2+-+4%2A1%2A3%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"m+=+%28-5+%2B+sqrt%285%5E2+-+4%2A1%2A3%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And this simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-5+%2B+sqrt%2825+-+12%29%29%2F2 ALIGN=MIDDLE  ALT=\"m+=+%28-5+%2B+sqrt%2825+-+12%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which simplifies even further to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-5+%2B+sqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"m+=+%28-5+%2B+sqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the other solution for m is exactly the same with the exception that the plus <BR>\n" );
document.write( "sign between the two terms changes to a minus sign.  Therefore, the other solution is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28-5+-+sqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"m+=+%28-5+-+sqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I hope that this shows you an understandable way to work quadratic equations using the<BR>\n" );
document.write( "quadratic formula to generate the solutions.  The quadratic formula is a method that will<BR>\n" );
document.write( "work on any quadratic equation. </SPAN>\n" );
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