document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=809383>Question 809383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the factors for the product of -36 and the sum of 12?<BR>\n" );
document.write( "The original problem was \r<BR>\n" );
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document.write( "2q/2q+3 -2q/2q-3=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #487588 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=487588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not all quadratic equations can be solved by factoring.<BR>\n" );
document.write( "Factoring works when the solutions are rational numbers.<BR>\n" );
document.write( "That is not the case for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4q%5E2%2B12q-9=0 ALIGN=MIDDLE  ALT=\"4q%5E2%2B12q-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "I would solve that by completing the square,<BR>\n" );
document.write( "or by applying the quadratic formula.<BR>\n" );
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document.write( "Completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4q%5E2%2B12q-9=0 ALIGN=MIDDLE  ALT=\"4q%5E2%2B12q-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4q%5E2%2B12q=9 ALIGN=MIDDLE  ALT=\"4q%5E2%2B12q=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4q%5E2%2B12q ALIGN=MIDDLE  ALT=\"4q%5E2%2B12q\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you realize that it is part of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q%2B3%29%5E2=4q%5E2%2B12q%2B9 ALIGN=MIDDLE  ALT=\"2q%2B3%29%5E2=4q%5E2%2B12q%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so you add 9 to both sides of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4q%5E2%2B12q=9 ALIGN=MIDDLE  ALT=\"4q%5E2%2B12q=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4q%5E2%2B12q%2B9=9%2B9 ALIGN=MIDDLE  ALT=\"4q%5E2%2B12q%2B9=9%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q%2B3%29%5E2=18 ALIGN=MIDDLE  ALT=\"2q%2B3%29%5E2=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Either<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q%2B3=sqrt%2818%29 ALIGN=MIDDLE  ALT=\"2q%2B3=sqrt%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q%2B3=3sqrt%282%29 ALIGN=MIDDLE  ALT=\"2q%2B3=3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q=-3%2B3sqrt%282%29 ALIGN=MIDDLE  ALT=\"2q=-3%2B3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28q=%28-3%2B3sqrt%282%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28q=%28-3%2B3sqrt%282%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q%2B3=-sqrt%2818%29 ALIGN=MIDDLE  ALT=\"2q%2B3=-sqrt%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q%2B3=-3sqrt%282%29 ALIGN=MIDDLE  ALT=\"2q%2B3=-3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2q=-3-3sqrt%282%29 ALIGN=MIDDLE  ALT=\"2q=-3-3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28q=%28-3-3sqrt%282%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28q=%28-3-3sqrt%282%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both solutions can bew expressed with the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28q=%28-3+%2B-+3sqrt%282%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28q=%28-3+%2B-+3sqrt%282%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Applying the quadratic formula works well too, but it is kind of boring.<BR>\n" );
document.write( "(I only use it when the square to be completed is not too obvious).<BR>\n" );
document.write( "Assuming that you remember the formula and apply it flawlessly, you end up with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=%28-12+%2B-+sqrt%28288%29%29%2F8=%28-3%2A4+%2B-+sqrt%28144%2A2%29%29%2F%282%2A4%29=%28-3%2A4+%2B-+sqrt%28144%29%2Asqrt%282%29%29%2F%282%2A4%29=%28-3%2A4+%2B-+12%2Asqrt%282%29%29%2F%282%2A4%29=%28-3%2A4+%2B-+3%2A4%2Asqrt%282%29%29%2F%282%2A4%29=%0D%0A4%2A%28-3+%2B-+3%2Asqrt%282%29%29%2F%282%2A4%29=highlight%28%28-3+%2B-+3sqrt%282%29%29%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );