SOLUTION: What value of c makes x^2 +5x+c a perfect square. I know the answer is 25/4 but I'm not confident with these type of questions,can someone please explain?

Question 122470: What value of c makes x^2 +5x+c a perfect square. I know the answer is 25/4 but I'm not confident with these type of questions,can someone please explain?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

You're correct and here's why.
Let's look at a perfect square.

When you expand the perfect square using the FOIL method (First Outer Inner Last), you get

If you look at the x coefficient in the right hand side, it's .
If you look at the constant term, it's
If you know the x coefficient, then you can get to the constant term.
You take half of it and square it.
In your case, the constant term is 5.
Half of is .
The square of that is .
Similarly if you know the constant term, you can get to the x coefficient.
If your equation was

You can take the constant term, 9, and find the square root and double it to get the x coefficient for the perfect square.
or
The x coefficient would then be c=2(3)=6 or c=2(-3)=-6

Hope that helped.

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