document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=352786>Question 352786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x squared-8x-29=(this equal sign has 3 lines)(x+a)squared+b, where a and b are constants. find the value of a and the value of b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #252165 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=252165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ -\ 29\ \equiv\ (x\ +\ a)^2\ +\ b\">\r<BR>\n" );
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document.write( "This is a \"Complete the Square\" problem.\r<BR>\n" );
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document.write( "Start by setting the LHS equal to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ -\ 29\ =\ 0\">\r<BR>\n" );
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document.write( "Add the opposite of the constant term to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ =\ 29\">\r<BR>\n" );
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document.write( "Divide the coefficient on the first degree term by 2, square the result, and then add that result to both sides.  -8 divided by 2 is -4.  -4 squared is 16.  Add 16 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ +\ 16\ =\ 29\ +\ 16\">\r<BR>\n" );
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document.write( "The quadradic trinomial in the LHS is now a perfect square.  Factor it:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 4)^2\ =\ 45\">\r<BR>\n" );
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document.write( "Add the opposite of the constant term to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 4)^2\ -\ 45\ =\ 0\">\r<BR>\n" );
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document.write( "Since both the original LHS and this new LHS are equal to zero, they must be equivalent, hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ -\ 29\ \equiv\ (x\ +\ (-4))^2\ +\ (-45)\">\r<BR>\n" );
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document.write( "But the original LHS was equivalent to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ a)^2\ +\ b\">, hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ +\ a)^2\ +\ b\ \equiv\ (x\ +\ (-4))^2\ +\ (-45)\">\r<BR>\n" );
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document.write( "Therefore:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ -4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ -45\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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