Final answer:
The value of c that makes x^2 + 6x + c a perfect square trinomial is 9.
Step-by-step explanation:
A perfect square trinomial has the form (x + a)^2, where a represents a constant. To determine the value of c that makes x^2 + 6x + c a perfect square trinomial, we need to find the value of a. We can do this by completing the square. In this case, let's take the coefficient of x, which is 6, divide it by 2, and square it. (6/2)^2 = 9. Therefore, the value of c that makes x^2 + 6x + c a perfect square trinomial is 9.
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