Final answer:
The value of c that makes the equation x^2 - 16x + c a perfect square is 64, as it is the square of half the coefficient of x (which is -16).
Step-by-step explanation:
The student asked to find the value of c that makes the equation x^2 - 16x + c a perfect square. To form a perfect square trinomial from a quadratic expression of the form x^2 + bx + c, the constant c needs to be equal to the square of half of the coefficient of x, which in this problem is -16. Therefore, we take (-16/2)^2 to find the value of c.
Thus, the value of c that makes x^2 - 16x + c a perfect square is 64, which corresponds to option a) c = 64.