document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=530118>Question 530118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve:\r<BR>\n" );
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document.write( "Find all real solutions of the given equation:\r<BR>\n" );
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document.write( "(x^2 - x)^2 - 63(x^2-x) - 648 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #349908 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=349908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Check my arithmetic, because I'm error prone, and sometimes my + and - sihgn magically inerconvert.<BR>\n" );
document.write( "I would start by doing a variable change by defining<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-x ALIGN=MIDDLE  ALT=\"y=x%5E2-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then the equation is really<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-63y-648=0 ALIGN=MIDDLE  ALT=\"y%5E2-63y-648=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+72 ALIGN=MIDDLE  ALT=\"y+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-9 ALIGN=MIDDLE  ALT=\"y=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you would have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x=72 ALIGN=MIDDLE  ALT=\"x%5E2-x=72\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with two real solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x=-9 ALIGN=MIDDLE  ALT=\"x%5E2-x=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "that would lead you to two other complex solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281+%2B-+i%2Asqrt%2835%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%281+%2B-+i%2Asqrt%2835%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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