document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65134>Question 65134</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by completing the square.  Show your steps: 2x^2 - 3x + 5 = 0    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45618 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=45618\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve by completing the square.  Show your steps: \r<BR>\n" );
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document.write( "2x^2 - 3x + 5 = 0  First we'll divide both sides by 2.  Why?  Because in the standard form of the quadratic equation (Ax^2+Bx+C=0). I find the problem easier if A is 1.  Also, if the quadratic is factorable and A is 1 then B is the sum of the products of C.\r<BR>\n" );
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document.write( "Dividing by 2 we get:\r<BR>\n" );
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document.write( "x^2-(3/2)x+5/2=0 subtract 5/2 from both sides:\r<BR>\n" );
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document.write( "x^2-(3/2)x=-5/2  If we take 1/2 of the B term (1/2)(3/2), <BR>\n" );
document.write( "square it ((1/2)(3/2))^2 and add it to both sides, the left side will be a perfect square.\r<BR>\n" );
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document.write( "((1/2)(3/2))^2=(3/4)^2=9/16. Now we'll add this to both sides and we have:\r<BR>\n" );
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document.write( "x^2-(3/2)x+9/16=-5/2+9/16 =-40/16+9/16 simplifying\r<BR>\n" );
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document.write( "x^2-(3/2)x+9/16=-31/16 Factoring the left side we get:\r<BR>\n" );
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document.write( "(x-3/4)^2=-31/16  Take sqrt of both sides:\r<BR>\n" );
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document.write( "x-3/4=+or-sqrt(-31/16) =+or-((i)sqrt(31)/4  Now add 3/4 to both sides:\r<BR>\n" );
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document.write( "x=3/4+or-((i)sqrt(31))/4  so we have:\r<BR>\n" );
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document.write( "x=(3+(i)sqrt(31))/4<BR>\n" );
document.write( "x=(3-(i)sqrt(31))/4\r<BR>\n" );
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document.write( "Hope this helps some.  Happy holidays-----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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