SOLUTION: Factor the expression: x^2 - 7x + 10

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Question 397833: Factor the expression: x^2 - 7x + 10
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can do this by completing the square.
x%5E2+-+7x+=+-10
x%5E2+-+7x+%2B+%287%2F2%29%5E2+=+-+10+%2B+%287%2F2%29%5E2
x%5E2+-+7x+%2B+49%2F4+=+-+40%2F4+%2B+49%2F4
Now both sides are a perfect square
%28x+-+7%2F2%29%5E2+=+%283%2F2%29%5E2
Take the square root of both sides
(1) x+-+7%2F2+=+3%2F2
and
(2) x+-+7%2F2+=+-3%2F2
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solving:
(1) x+=+7%2F2+%2B+3%2F2
(1) x+=+5
and
(2) x+-+7%2F2+=+-3%2F2
(2) x+=+7%2F2+-+3%2F2
(2) x+=+2
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Then
x+-+5+=+0
x+-+2+=+0
therefore
%28x+-+2%29%2A%28x+-+5%29+=+x%5E2+-+7x+%2B+10