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?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> 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?      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B5x%2Bc
You're correct and here's why.
Let's look at a perfect square.
%28x%2Ba%29%5E2
When you expand the perfect square using the FOIL method (First Outer Inner Last), you get
%28x%2Ba%29%5E2=%28x%2Ba%29%28x%2Ba%29
%28x%2Ba%29%5E2=%28x%29%28x%29%2B%28x%29%28a%29%2B%28a%29%28x%29%2B%28a%29%28a%29
%28x%2Ba%29%5E2=x%5E2%2Bax%2Bax%2Ba%5E2
%28x%2Ba%29%5E2=x%5E2%2Bhighlight%282a%29x%2Bhighlight%28a%5E2%29
If you look at the x coefficient in the right hand side, it's 2a.
If you look at the constant term, it's a%5E2
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 5 is 5%2F2.
The square of that is highlight%2825%2F4%29.
Similarly if you know the constant term, you can get to the x coefficient.
If your equation was
x%5E2%2Bcx%2B9
You can take the constant term, 9, and find the square root and double it to get the x coefficient for the perfect square.
sqrt%289%29=3 or sqrt%289%29=-3
The x coefficient would then be c=2(3)=6 or c=2(-3)=-6
x%5E2%2B6x%2B9=%28x%2B3%29%5E2
x%5E2-6x%2B9=%28x-3%29%5E2
Hope that helped.