Find the value of c that completes the square
X^2+17x+c
To complete the square for the quadratic expression x^2 + 17x + c, we need to add and subtract (17/2)^2 = (289/4) to the expression.
Completing the square, we have:
x^2 + 17x + c = x^2 + 17x + 289/4 - 289/4 + c
= (x^2 + 17x + 289/4) - 289/4 + c
= (x + 17/2)^2 - 289/4 + c
Now, for the quadratic to be a perfect square trinomial, we need the constant term to be -(289/4) + c = 0.
Therefore, c = 289/4.