Final answer:
To complete the square for the function f(x) = x^2 + 36x + c, we calculate (36/2)^2, which equals 324. Therefore, the value of c that completes the square is 324.
Step-by-step explanation:
The question asks to find the value of c that completes the square for the quadratic function f(x) = x^2 + 36x + c. To complete the square, we need to add a value to the equation that allows it to be written in the form of (x + a)^2. In this format, a is equal to half of the coefficient of the x term. Therefore, we take half of 36, which is 18, and then square it to get 324. The value of c that completes the square is 324, making the function a perfect square trinomial, f(x) = (x+18)^2.