document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=756600>Question 756600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION<BR>\n" );
document.write( "x^3 &#8722; 7x^2 + 6x &#8722; 47 = x^2 + 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #460391 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=460391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^3 &#8722; 7x^2 + 6x &#8722; 47 = x^2 + 1<BR>\n" );
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document.write( "x^3 - 7x^2 - x^2 + 6x - 47 - 1 = 0<BR>\n" );
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document.write( "x^3 - 8x^2 + 6x - 48 = 0<BR>\n" );
document.write( "Group factor<BR>\n" );
document.write( "x^2(x - 8) + 6(x - 8) = 0<BR>\n" );
document.write( "Factor out (x-8)<BR>\n" );
document.write( "(x - 8)(x^2 + 6) = 0<BR>\n" );
document.write( "Solutions<BR>\n" );
document.write( "x = 8, the only real solution<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x^2 = -6; non-real solutions<BR>\n" );
document.write( "x = +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-6%29 ALIGN=MIDDLE  ALT=\"sqrt%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"i%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"i%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check in original problem with x=8<BR>\n" );
document.write( "x^3 - 7x^2 + 6x - 47 = x^2 + 1<BR>\n" );
document.write( "8^3 - 7(8^2) + 6(8) - 47 = 8^2 + 1<BR>\n" );
document.write( "512 - 448 + 48 - 47 = 64 + 1<BR>\n" );
document.write( "65 = 65; confirms our solution </SPAN>\n" );
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