document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762754>Question 762754</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=x%5E9%2B2x%5E8%2Bx%5E7%2B6x%5E6%2B7x%5E5-2x%5E4%2B3x%5E3%2B2x%5E2-12x-8=0 ALIGN=MIDDLE  ALT=\"x%5E9%2B2x%5E8%2Bx%5E7%2B6x%5E6%2B7x%5E5-2x%5E4%2B3x%5E3%2B2x%5E2-12x-8=0\"   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 #464189 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=464189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The only way to solve this (or any other polynomial equation of degree 5 or greater) is by numerical approximation.  I graphed it and saw that there is a root very near -2, possible multiple roots at -1, and a root at 1.\r<BR>\n" );
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document.write( "A little polynomial long division gets you to the following result:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ +\ 1)^3(x\ -\ 1)(x\ +\ 2)(x^4\ -\ 2x^3\ +\ 5x\ -\ 4x\ +\ 4)\ =\ 0\">\r<BR>\n" );
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document.write( "Plugging the coefficients of the quartic factor into an on-line <a  rel=nofollow HREF=\"http://www.akiti.ca/Quad4Deg.html\">Quartic Solver</a>, I got the following results:\r<BR>\n" );
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document.write( "0.5   +   1.323 i<BR>\n" );
document.write( "0.5   -   1.323 i<BR>\n" );
document.write( "0.5   +   1.323 i<BR>\n" );
document.write( "0.5   -   1.323 i\r<BR>\n" );
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document.write( "One pair of complex conjugates with a multiplicity of 2.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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