document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237819>Question 237819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve qudratic equation.\r<BR>\n" );
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document.write( "(x^2-7)^2+3(x^2-7)+2=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174837 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=174837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Use a substitution:\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large u\ =\ x^2\ -\ 7\">\r<BR>\n" );
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document.write( "Now the problem becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ u^2\ +\ 3u\ -\ 12\ =\ 0\">\r<BR>\n" );
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document.write( "Which, more's the pity, does not factor.\r<BR>\n" );
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document.write( "Use the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ u = \frac{-(3) \pm sqrt{(3)^2 - 4(1)(-12)}}{2(1)}\ =\ \frac{-3\ \pm\ 3\sqrt{5}}{2}\">\r<BR>\n" );
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document.write( "(Verification left as an exercise for the student)\r<BR>\n" );
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document.write( "But now we have to go back and unwind the substitution:\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large u\ =\ x^2\ -\ 7\">,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 7\ =\ \frac{-3\ \pm\ 3\sqrt{5}}{2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ =\ \frac{11\ \pm\ 3\sqrt{5}}{2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \pm\sqrt{\frac{11\ \pm\ 3\sqrt{5}}{2}}\">\r<BR>\n" );
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document.write( "Yes, that is uglier than a mud fence.  Notice that you actually have four roots. This is, of course, to be expected because this equation began life as a quartic not a quadratic.\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" );
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