document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305085>Question 305085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I complete the square?<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 #218485 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=218485\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 + 6x + 23 = 0\r<BR>\n" );
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document.write( "Rewrie the above as:\r<BR>\n" );
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document.write( "x^2 + 6x = -23\r<BR>\n" );
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document.write( "To complete the square on the loeft side we need to divide the coefficient on the x term by 2,  square it and add the result to both sides:\r<BR>\n" );
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document.write( "The coefficient on the x term is 6, so we have (6/2)^2 = 3^2 = 9. Adding 9 to both sides we have:\r<BR>\n" );
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document.write( "x^2 + 6x + 9 = -23 + 9\r<BR>\n" );
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document.write( "x^2 + 6x + 9 = -14\r<BR>\n" );
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document.write( "(x+3)*(x+3) = -14<BR>\n" );
document.write( "(x+3)^2 = -14\r<BR>\n" );
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document.write( "Taking the square root of both sides:\r<BR>\n" );
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document.write( "(x+3)= +sqrt(-14) and<BR>\n" );
document.write( "(x+3)= -sqrt(-14)\r<BR>\n" );
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document.write( "Note that sqrt(-14) is a complex number, namely i*sqrt(14).\r<BR>\n" );
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document.write( "We have then:\r<BR>\n" );
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document.write( "x+3 = i*sqrt(14)<BR>\n" );
document.write( "x = -3 + i*sqrt914)\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "x+3 = -i*sqrt(14)<BR>\n" );
document.write( "x = -3 - i*sqrt(14)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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