document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=837887>Question 837887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the solution for x?\r<BR>\n" );
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document.write( "sqrt(x+5)=x^2-5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521690 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=521690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The solution is very long a little tough...but I will summarize...\r<BR>\n" );
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document.write( "square both sides to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-5%29%5E2=x%2B5 ALIGN=MIDDLE  ALT=\"%28x%5E2-5%29%5E2=x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify and rewrite as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=x%5E4-10x%5E2-x%2B20 ALIGN=MIDDLE  ALT=\"P=x%5E4-10x%5E2-x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We wish to write this as a product of square polynomials, so after some careful thought and experimentation we use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%28x%5E2-a%29%5E2-%28bx%2Bc%29%5E2 ALIGN=MIDDLE  ALT=\"P=%28x%5E2-a%29%5E2-%28bx%2Bc%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When we expand this version and compare coefficients we can determine that\r<BR>\n" );
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document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2a-b%5E2=-10 ALIGN=MIDDLE  ALT=\"-2a-b%5E2=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2bc=-1 ALIGN=MIDDLE  ALT=\"-2bc=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-c%5E2=20 ALIGN=MIDDLE  ALT=\"a%5E2-c%5E2=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This nonlinear can be solved by substitution. It has a rational solution of \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=9%2F2 ALIGN=MIDDLE  ALT=\"a=9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=1%2F2 ALIGN=MIDDLE  ALT=\"c=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "therefore we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%28x%5E2-9%2F2%29%5E2-%28x%2B1%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"P=%28x%5E2-9%2F2%29%5E2-%28x%2B1%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and that means\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-10x%5E2-x%2B20=%28x%5E2-9%2F2%29%5E2-%28x%2B1%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E4-10x%5E2-x%2B20=%28x%5E2-9%2F2%29%5E2-%28x%2B1%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-10x%5E2-x%2B20=%28x%5E2%2Bx-5%29%28x%5E2%2Bx-4%29 ALIGN=MIDDLE  ALT=\"x%5E4-10x%5E2-x%2B20=%28x%5E2%2Bx-5%29%28x%5E2%2Bx-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we know there are only two solutions so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1-sqrt%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-1-sqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2Bsqrt%2821%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%281%2Bsqrt%2821%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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