document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909147>Question 909147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2-4x-8%29%28x%5E2-4x%29=48+ ALIGN=MIDDLE  ALT=\"+%28x%5E2-4x-8%29%28x%5E2-4x%29=48+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551646 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=551646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hopefully, simplification will allow an equation in quadratic form.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4x-8%29%28x%5E2-4x%29=48 ALIGN=MIDDLE  ALT=\"%28x%5E2-4x-8%29%28x%5E2-4x%29=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-4x%5E3-8x%5E2-4x%5E3%2B16x%5E2%2B32x-48=0 ALIGN=MIDDLE  ALT=\"x%5E4-4x%5E3-8x%5E2-4x%5E3%2B16x%5E2%2B32x-48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-8x%5E3%2B8x%5E2%2B32x-48=0 ALIGN=MIDDLE  ALT=\"x%5E4-8x%5E3%2B8x%5E2%2B32x-48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Forget about quadratic form.  Look for roots.<BR>\n" );
document.write( "Check plus and minus of -1,2,4,6,8,24.  (Rational Roots Theorem, synthetic division).\r<BR>\n" );
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document.write( "-2 is a root, giving coefficients 1,-10,28,-24.<BR>\n" );
document.write( "2 is a root, giving coefficients 1,-8,12, which now represents a quadratic factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B12 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now you can try to factorize for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B12=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x-6%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Indicating the last two roots are 2 and 6.\r<BR>\n" );
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document.write( "The original equation is equivalent to  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-2%29%29%28x-2%29%28x-2%29%28x-6%29=0 ALIGN=MIDDLE  ALT=\"%28x-%28-2%29%29%28x-2%29%28x-2%29%28x-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x%2B2%29%28x-2%29%5E2%28x-6%29=0%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x%2B2%29%28x-2%29%5E2%28x-6%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The solution then is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "The root, x=2 occurs twice, so this has a MULTIPLICITY OF 2. </SPAN>\n" );
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