document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191107>Question 191107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> COMPLETING THE SQUARE 5-5\r<BR>\n" );
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document.write( "            Solving a quadratic equation if the coefficient of x^2 is 1\r<BR>\n" );
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document.write( "               x^2=4x-13 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143453 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=143453\">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( "By the numbers:\r<BR>\n" );
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document.write( "<b>Step 1:</b> Variables on the left, constants on the right.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2-4x=-13 \">\r<BR>\n" );
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document.write( "<b>Step 2:</b> Divide the coefficient on the 1st order term by 2, square the result, add that result to both sides of the equation (-4 divided by 2 is -2, -2 squared is 4, so add 4 to each side):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2-4x + 4=-13+4 = -9 \">\r<BR>\n" );
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document.write( "<b>Step 3:</b> Now that we have 'completed the square' by creating a perfect square trinomial on the left, factor it:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x - 2)^2 = -9 \">\r<BR>\n" );
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document.write( "<b>Step 4:</b> Take the square root:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x - 2 = \pm sqrt{-9}\">\r<BR>\n" );
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document.write( "Clang! Buzz-Buzz-Buzz! Warning, Will Robinson!  We have a negative radicand.\r<BR>\n" );
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document.write( "<b>Step 5:</b>  Factor the -1 out of the radicand:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x - 2 = \pm sqrt{(-1)(9)}\">\r<BR>\n" );
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document.write( "<b>Step 6:</b> Use the definition of the imaginary number <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE i\">,namely <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE i^2 = -1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x - 2 = \pm 3i\">\r<BR>\n" );
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document.write( "<b>Step 7:</b> Add 2 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 \pm 3i\">\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" );
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