document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=760427>Question 760427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all the real solutions to the equation:  |x^(2) -8|=|9-x|-1. Provide exact solutions (not rounded numbers) please and thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #462649 by </B><A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><B>tommyt3rd(5050)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><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=tommyt3rd><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=462649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve we need to find a way to address the absolute values. We can use the definition:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Aabs%28x%5E2-8%29=abs%289-x%29-1%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Aabs%28x%5E2-8%29=abs%289-x%29-1%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that means there are four possibilities:\r<BR>\n" );
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document.write( "1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Ax%5E2-8=9-x-1%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Ax%5E2-8=9-x-1%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which leads to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Ax+=+%28-1+%2B-+sqrt%2865%29%29%2F2%0D%0A+ ALIGN=MIDDLE  ALT=\"%0D%0Ax+=+%28-1+%2B-+sqrt%2865%29%29%2F2%0D%0A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Ax%5E2-8=x-9-1%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Ax%5E2-8=x-9-1%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which yields complex roots\r<BR>\n" );
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document.write( "3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Ax%5E2-8=9-x%2B1%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Ax%5E2-8=9-x%2B1%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which yields extraneous roots\r<BR>\n" );
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document.write( "4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Ax%5E2-8=x-9%2B1%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0Ax%5E2-8=x-9%2B1%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which yields <BR>\n" );
document.write( "x=0, x=1\r<BR>\n" );
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document.write( ":) </SPAN>\n" );
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