document.write( "Question 65105: Solve the equation by completing the square. x^2-4x+3=0
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Algebra.Com's Answer #45659 by ptaylor(2198)\"\" \"About 
You can put this solution on YOUR website!
Solve the equation by completing the square. \r
\n" ); document.write( "\n" ); document.write( "(1) x^2-4x+3=0 First, lets add -3 to both sides and we have:\r
\n" ); document.write( "\n" ); document.write( "x^2-4x=-3 \r
\n" ); document.write( "\n" ); document.write( "Now why did we do that? If you look at the left side of the equation only, you will see that its actually a quadratic equation that's missing the \"C\" term. We are going to choose a new \"C\" for the left side of the equation and add it to both sides thereby creating a new quadratic equation on the left side that's a perfect square.\r
\n" ); document.write( "\n" ); document.write( "We'll take 1/2 of the \"B\" term(1/2)(4) or 2 and square it (2^2=4) and add this to both sides of the equation:\r
\n" ); document.write( "\n" ); document.write( "x^2-4x+4=-3+4 or
\n" ); document.write( "(x-2)^2=1 take sqrt of both sides
\n" ); document.write( "x-2=+or-sqrt(1) or
\n" ); document.write( "x-2=+or-1 now add 2 to both sidess
\n" ); document.write( "x=2+or-1
\n" ); document.write( "x=2+1=3 and
\n" ); document.write( "x=2-1=1\r
\n" ); document.write( "\n" ); document.write( "ck
\n" ); document.write( "substitute in (1)
\n" ); document.write( "3^2-4(3)+3=0
\n" ); document.write( "9-12+3=0
\n" ); document.write( "-3+3=0
\n" ); document.write( "0=0
\n" ); document.write( "1^2-4(1)+3=0
\n" ); document.write( "1-4+3=0
\n" ); document.write( "-3+3=0
\n" ); document.write( "0=0 \r
\n" ); document.write( "\n" ); document.write( "Hope this helps. Happy holidays---ptaylor\r
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