SOLUTION: x^2-5x+(25/4)

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Question 403034: x^2-5x+(25/4)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First let's review one of the factoring patterns: %28a-b%29%28a-b%29+=+a%5E2+-2ab+%2B+b%5E2. The first term is a prefect square. It is the square of a. The last term is also a perfect square, It is the square of b. And the middle term subtracted and it is 2 times the a times the b.

Now let's look at your expression:
x%5E2+-+5x+%2B+%2825%2F4%29
Your first term is a perfect square. It is the square of x. So "x" is our "a". The last term is a perfect square. It is the square of 5/2. (Think about it.) So 5/2 is our "b". The middle term is subtracted and it is 2 times the "a" times the "b":
2*x*(5/2) = 5x
Looking at your expression this way we can now see how to factor is according to the pattern:
x%5E2-5x%2B%2825%2F4%29+=+%28x-5%2F2%29%28x-5%2F2%29
or
x%5E2-5x%2B%2825%2F4%29+=+%28x-5%2F2%29%5E2