SOLUTION: Find the constant term that should be added to make the following expression a perfect-square trinomial. x2 + 5x

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Question 49408: Find the constant term that should be added to make the following expression a perfect-square trinomial.
x2 + 5x
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
To make this binomial x%5E2%2B5x into a perfect square trinomial, simply add the square of half the coefficient of the x-term. So you would add: %285%2F2%29%5E2+=+25%2F4
The trinomial becomes:
x%5E2%2B5x%2B25%2F4 If you now factor this, you can see that it is a perfect square.
x%5E2%2B5x%2B25%2F4+=+%28x%2B5%2F2%29%5E2 Check using FOIL.
%28x%2B5%2F2%29%28x%2B5%2F2%29+=+x%5E2%2B%285%2F2%29x%2B%285%2F2%29x%2B25%2F4 Simplify to: x%5E2%2B5x%2B25%2F4