document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1057496>Question 1057496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using \"Completing the Square\" to find ALL solutions for: X^2-6x=40\r<BR>\n" );
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document.write( "How do you find ALL solutions?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #672533 by </B><A HREF=/tutors/aboutme.mpl?userid=solve_for_x><B>solve_for_x(190)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solve_for_x><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=672533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Complete the square by adding the square of half of the coefficient of the \"x\"-term to both sides.\r<BR>\n" );
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document.write( "x^2 - 6x = 40\r<BR>\n" );
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document.write( "The coefficient of the x term is -6. Half of that is -3. And -3 squared is 9.\r<BR>\n" );
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document.write( "Adding 9 to both sides gives:\r<BR>\n" );
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document.write( "x^2 - 6x + 9 = 49\r<BR>\n" );
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document.write( "The left side can be factored as a perfect square:\r<BR>\n" );
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document.write( "(x - 3)^2 = 49\r<BR>\n" );
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document.write( "Taking the square root of both sides then gives:\r<BR>\n" );
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document.write( "x - 3 = ±7\r<BR>\n" );
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document.write( "Adding 3 to both sides gives solutions for x:\r<BR>\n" );
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document.write( "x = 3 ± 7\r<BR>\n" );
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document.write( "The solutions are:\r<BR>\n" );
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document.write( "x = 3 - 7 = -4\r<BR>\n" );
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document.write( "x = 3 + 7 = 10\r<BR>\n" );
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document.write( "Thus, the set of solutions is x = -4 and x = 10.\r<BR>\n" );
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document.write( "You can confirm this by rearranging the original equation as x^2 - 6x - 40 = 0, and then<BR>\n" );
document.write( "using the Quadratic Formula to get the solutions for x. </SPAN>\n" );
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