Question 65105: Solve the equation by completing the square. x^2-4x+3=0
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Solve the equation by completing the square.
(1) x^2-4x+3=0 First, lets add -3 to both sides and we have:
x^2-4x=-3
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.
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:
x^2-4x+4=-3+4 or
(x-2)^2=1 take sqrt of both sides
x-2=+or-sqrt(1) or
x-2=+or-1 now add 2 to both sidess
x=2+or-1
x=2+1=3 and
x=2-1=1
ck
substitute in (1)
3^2-4(3)+3=0
9-12+3=0
-3+3=0
0=0
1^2-4(1)+3=0
1-4+3=0
-3+3=0
0=0
Hope this helps. Happy holidays---ptaylor
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