document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=722631>Question 722631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please show me the steps to factoring and solving the problem below?  \r<BR>\n" );
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document.write( "Also, could you please show me how to check my solution back into the original equation?\r<BR>\n" );
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document.write( "Could you please show me the final solutions as decimal approximations carried out to the third decimal place.\r<BR>\n" );
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document.write( "If possible and applicable, could you please show me how to incorporate the following four math vocabulary words into my steps?\r<BR>\n" );
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document.write( "-Quadratic formula <BR>\n" );
document.write( "-Factoring <BR>\n" );
document.write( "-Completing the square <BR>\n" );
document.write( "-Discriminant \r<BR>\n" );
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document.write( "1.	2m^(2) - m - 15 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #442952 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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/cgi-bin/show-face.mpl?user=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=442952\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2-m-15 ALIGN=MIDDLE  ALT=\"2m%5E2-m-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "factoring\r<BR>\n" );
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document.write( "coefficient of middle term is -1\r<BR>\n" );
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document.write( "the product of first term and third term is 30\r<BR>\n" );
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document.write( "find two factors of 30 such that when you add them you get -1\r<BR>\n" );
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document.write( "Obviously they are -6and +5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2-6m%2B5m-15=0 ALIGN=MIDDLE  ALT=\"2m%5E2-6m%2B5m-15=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=2m%28m-3%29%2B5%28m-3%29=0 ALIGN=MIDDLE  ALT=\"2m%28m-3%29%2B5%28m-3%29=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=%282m%2B5%29%28m-3%29=0 ALIGN=MIDDLE  ALT=\"%282m%2B5%29%28m-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "either 2m+5 =0 OR m-3=0 for the equation to be true\r<BR>\n" );
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document.write( "if 2m+5 = 0<BR>\n" );
document.write( "then 2m=-5<BR>\n" );
document.write( "m=-5/2\r<BR>\n" );
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document.write( "if m-3 =0<BR>\n" );
document.write( "then m=3\r<BR>\n" );
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document.write( "so m=-5/2 or 3\r<BR>\n" );
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document.write( "completing the squares method\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E2-m-15=0 ALIGN=MIDDLE  ALT=\"2m%5E2-m-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the first term co efficient has to be  1<BR>\n" );
document.write( "divide by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2-%28m%2F2%29+-%2815%2F2%29=0 ALIGN=MIDDLE  ALT=\"m%5E2-%28m%2F2%29+-%2815%2F2%29=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=m%5E2-%28m%2F2%29+=%2815%2F2%29 ALIGN=MIDDLE  ALT=\"m%5E2-%28m%2F2%29+=%2815%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find the third term on the left side so that it is a perfect square<BR>\n" );
document.write( "third term = (1/2 * co-efficient of second term)^2\r<BR>\n" );
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document.write( "=(1/2*1/2)^2<BR>\n" );
document.write( "= 1/16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2-%28m%2F2%29+=%2815%2F2%29 ALIGN=MIDDLE  ALT=\"m%5E2-%28m%2F2%29+=%2815%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add the third term to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2-%28m%2F2%29%2B%281%2F16%29+=%2815%2F2%29%2B%281%2F16%29 ALIGN=MIDDLE  ALT=\"m%5E2-%28m%2F2%29%2B%281%2F16%29+=%2815%2F2%29%2B%281%2F16%29\"   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=%28m-%281%2F4%29%29%5E2=+-121%2F16 ALIGN=MIDDLE  ALT=\"%28m-%281%2F4%29%29%5E2=+-121%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "take the square root\r<BR>\n" );
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document.write( "m-(1/4) = +/- 11/4\r<BR>\n" );
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document.write( "so m= 3 or -<BR>\n" );
document.write( "5/2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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