document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65430>Question 65430</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/093979862x/algebrahomeworkh>An Incremental Development</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Solve by completing the square\r<BR>\n" );
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document.write( "3x^2 - 4x + 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 #46050 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=46050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve by completing the square\r<BR>\n" );
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document.write( "3x^2 - 4x + 5 = 0 \r<BR>\n" );
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document.write( "First, divide both sides by 3. (We want the coefficient of x^2 to be 1.  This will simplify completing the square).  We get:\r<BR>\n" );
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document.write( "x^2-(4/3)x+(5/3)=0\r<BR>\n" );
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document.write( "Next, subtract (5/3) from both sides. This removes the \"C\" term from the left side.  We will now choose another \"C\" term that will result in a perfect square on the left side and then we will add it to both sides:\r<BR>\n" );
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document.write( "x^2-(4/3)x=-(5/3)\r<BR>\n" );
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document.write( "Now, we will complete the square.  Take half of the \"x\" coefficient (1/2)(4/3), square it ((1/2)(4/3))^2 and add it to both sides:<BR>\n" );
document.write( "((1/2)(4/3))^2=(4/6)^2=16/36 so we add 16/36 to both sides:\r<BR>\n" );
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document.write( "x^2-(4/3)x+(16/36)=-(5/3)+(16/36)\r<BR>\n" );
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document.write( "Let's simplify the right side of the equation<BR>\n" );
document.write( "-(5/3)+(16/36)=-(60/36)+(16/36)=-44/36\r<BR>\n" );
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document.write( "Note: the left side is a perfect square:<BR>\n" );
document.write( "(x-4/6)^2=-44/36\r<BR>\n" );
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document.write( "Take sqrt of both sides:<BR>\n" );
document.write( "x-4/6=+or-sqrt(-44/36)  add 4/6 to both sides:\r<BR>\n" );
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document.write( "x=(4/6)+or-((i)sqrt(44))/6 simplifying:<BR>\n" );
document.write( "x=(4+or-((i)sqrt(4)(11)))6 and this equals<BR>\n" );
document.write( "x=(4+or-(2i)sqrt(11))/6 or<BR>\n" );
document.write( "x=(2+(i)sqrt(11))/2<BR>\n" );
document.write( "x=(2-(i)sqrt(11))/2\r<BR>\n" );
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document.write( "Happy holidays----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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