Final answer:
To find the value of c that makes the trinomial x² - 14x + c a perfect square, we can complete the square. The value of c that makes the trinomial a perfect square is 49.
Step-by-step explanation:
To find the value of c that makes the trinomial x² - 14x + c a perfect square, we need to complete the square. The perfect square trinomial form is (x +/- d)² where d is half of the coefficient of x. In this case, half of -14 is -7, so the trinomial can be written as (x - 7)². Comparing this to the given expression, we can see that c = (-7)² = 49. Therefore, the value of c that makes the trinomial a perfect square is 49.