document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=624872>Question 624872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following equation by using an appropriate substitution <BR>\n" );
document.write( "(x^2-x)^2-18(x^2-x)+72=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #393173 by </B><A HREF=/tutors/aboutme.mpl?userid=Maths68><B>Maths68(1474)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Maths68><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=Maths68><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=393173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x^2-x)^2-18(x^2-x)+72=0\r<BR>\n" );
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document.write( "Let y=(x^2-x)\r<BR>\n" );
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document.write( "y^2-18y+72=0<BR>\n" );
document.write( "Now solve for y<BR>\n" );
document.write( "y^2-12y-6y+72=0<BR>\n" );
document.write( "y(y-12)-6(y-12)=0<BR>\n" );
document.write( "(y-12)(y-6)=0<BR>\n" );
document.write( "y-12=0 or y-6=0<BR>\n" );
document.write( "y=12 or y=6\r<BR>\n" );
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document.write( "Put the value of y in to above equations.<BR>\n" );
document.write( "y=12<BR>\n" );
document.write( "x^2-x=12 or x^2-x=6<BR>\n" );
document.write( "x^2-x-12=0 or x^2-x-6=0<BR>\n" );
document.write( "x^2-4x+3x-12=0 or x^2-3x+2x-6=0<BR>\n" );
document.write( "x(x-4)+3(x-4)=0 or x(x-3)+2(x-3)=0<BR>\n" );
document.write( "(x-4)(x+3)=0 or (x-3)(x+2)=0<BR>\n" );
document.write( "x-4=0 or x+3=0 or x-3=0 or x+2=0<BR>\n" );
document.write( "x=4 or x=-3 or x=3 or x=-2\r<BR>\n" );
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document.write( "Check<BR>\n" );
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document.write( "(x^2-x)^2-18(x^2-x)+72=0<BR>\n" );
document.write( "Put x=4<BR>\n" );
document.write( "((4)^2-4)^2-18((4)^2-4)+72=0<BR>\n" );
document.write( "(16-4)^2-18(16-4)+72=0<BR>\n" );
document.write( "(12)^2-18(12)+72=0<BR>\n" );
document.write( "144-216+72=0<BR>\n" );
document.write( "-72+72=0<BR>\n" );
document.write( "0=0\r<BR>\n" );
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document.write( "(x^2-x)^2-18(x^2-x)+72=0<BR>\n" );
document.write( "Put x=3<BR>\n" );
document.write( "((3)^2-3)^2-18((3)^2-3)+72=0<BR>\n" );
document.write( "(9-3)^2-18(9-3)+72=0<BR>\n" );
document.write( "(6)^2-18(6)+72=0<BR>\n" );
document.write( "36-108+72=0<BR>\n" );
document.write( "-72+72=0<BR>\n" );
document.write( "0=0\r<BR>\n" );
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document.write( "(x^2-x)^2-18(x^2-x)+72=0<BR>\n" );
document.write( "Put x=-3<BR>\n" );
document.write( "((-3)^2-(-3))^2-18((-3)^2-(-3))+72=0<BR>\n" );
document.write( "(9+3)^2-18(9+3)+72=0<BR>\n" );
document.write( "(12)^2-18(12)+72=0<BR>\n" );
document.write( "144-216+72=0<BR>\n" );
document.write( "-72+72=0<BR>\n" );
document.write( "0=0\r<BR>\n" );
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document.write( "(x^2-x)^2-18(x^2-x)+72=0<BR>\n" );
document.write( "Put x=-2<BR>\n" );
document.write( "((-2)^2-(-2))^2-18((-2)^2-(-2))+72=0<BR>\n" );
document.write( "(4+2)^2-18(4+2)+72=0<BR>\n" );
document.write( "(6)^2-18(6)+72=0<BR>\n" );
document.write( "(6)^2-18(6)+72=0<BR>\n" );
document.write( "36-108+72=0<BR>\n" );
document.write( "-72+72=0<BR>\n" );
document.write( "0=0 </SPAN>\n" );
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