document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=962474>Question 962474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.\r<BR>\n" );
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document.write( "1 + x + 2x2 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588073 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=588073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> start with 2x^2 + x + 1 = 0\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get:\r<BR>\n" );
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document.write( "2x^2 + x = -1\r<BR>\n" );
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document.write( "factor out a 2 on the left side of the equation to get:\r<BR>\n" );
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document.write( "2 * (x^2 + x/2) = -1\r<BR>\n" );
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document.write( "complete the squares on x^2 + x/2 to get:\r<BR>\n" );
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document.write( "2 * ((x+1/4)^2 - (1/16)) = -1\r<BR>\n" );
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document.write( "simplify by distibuting the multiplication to get:\r<BR>\n" );
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document.write( "2 * (x+1/4)^2 - 2*(1/16) = -1\r<BR>\n" );
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document.write( "simplify further to get:\r<BR>\n" );
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document.write( "2 * (x+1/4)^2 - 1/8 = -1\r<BR>\n" );
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document.write( "add 1/8 to both sides of the equation to get:\r<BR>\n" );
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document.write( "2 * (x + 1/4)^2 = -7/8\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get:\r<BR>\n" );
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document.write( "(x + 1/4)^2 = -7/16 ***** this is your solution.\r<BR>\n" );
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document.write( "continue further to solve for x if you care to, but the problem did not require you to do this.\r<BR>\n" );
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document.write( "take the square root of both sides of the equation to get:\r<BR>\n" );
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document.write( "x + 1/4 = plus or minus sqrt(-7/16)\r<BR>\n" );
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document.write( "subtract 1/4 from both sides of the equation to get x = -1/4 plus or minus sqrt(-7/16).\r<BR>\n" );
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document.write( "since sqrt(-7/16) is the same as sqrt(7/16) * i, your solution becomes:\r<BR>\n" );
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document.write( "x = -1/4 plus or minus sqrt(7/16) * i.\r<BR>\n" );
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document.write( "your problem was to convert it to the form of (x + p)2 = q.\r<BR>\n" );
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document.write( "the solution to that is:\r<BR>\n" );
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document.write( "(x + 1/4)^2 = -7/16\r<BR>\n" );
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document.write( "as indicated above with the *****\r<BR>\n" );
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document.write( " </SPAN>\n" );
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