document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123174>Question 1123174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rewrite the quadratic portion of the algebraic expression as the sum or difference of two squares by completing the square.<BR>\n" );
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document.write( "1/64 &#8722; 12x &#8722; x^2<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739481 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=739481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your expression is:\r<BR>\n" );
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document.write( "-x^2 - 12x + 1/64\r<BR>\n" );
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document.write( "set it equal to y and your equation is:\r<BR>\n" );
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document.write( "y = -x^2 - 12x + 1/64\r<BR>\n" );
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document.write( "set y equal to 0 and the equation becomes:\r<BR>\n" );
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document.write( "0 = -x^2 = 12x + 1/64\r<BR>\n" );
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document.write( "add -x^2 - 12x to both sides of the equation to get:\r<BR>\n" );
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document.write( "x^2 + 12x = 1/64\r<BR>\n" );
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document.write( "take half of the coefficient of the x term and subtract the square of half the coefficint of the x^2 term to form the following equation.\r<BR>\n" );
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document.write( "(x+6)^2 - 6^2 = 1/64\r<BR>\n" );
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document.write( "add 6^2 to both sides of the equation to get:\r<BR>\n" );
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document.write( "(x+6)^2 = 1/64 + 36\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "(x+6)^2 = 2305/64\r<BR>\n" );
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document.write( "the equation is now in completing the squares form.\r<BR>\n" );
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document.write( "take the square root of both sides of this equation to get:\r<BR>\n" );
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document.write( "x+6 = sqrt(2305/64)\r<BR>\n" );
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document.write( "subtract 6 from both sides to get:\r<BR>\n" );
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document.write( "x = sqrt(2305/64) - 6\r<BR>\n" );
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document.write( "if that solution is correct, then replacing x with that value in the original equation will make that equation true.\r<BR>\n" );
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document.write( "the original equation is -x^2 - 12x + 1/64 = 0\r<BR>\n" );
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document.write( "replacing x with sqrt(2305/64) - 6 results in:\r<BR>\n" );
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document.write( "-x^2 - 12x + 1/64 = 2.3 * 10^-14.\r<BR>\n" );
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document.write( "2.3 * 10^-14 is equal to a decimal point followed by 13 zeros followed by 23.\r<BR>\n" );
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document.write( "that looks  like .000000000000023 which is a very small number that you can safely assume would be equal to 0 if the calculator had more internal decimal digits to store.\r<BR>\n" );
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document.write( "i did confirm manually that the result is accurate and that replacing x with (sqrt(2305/64) - 6) does indeed lead to -x^2 - 12x + 1/64 = 0.\r<BR>\n" );
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document.write( "here's a reference on completing the squares method you might find useful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/sqrquad.htm\" target = \"_blank\">https://www.purplemath.com/modules/sqrquad.htm</a> </SPAN>\n" );
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