Final answer:
The value of c that will make 25x^2-40x+c a perfect square trinomial is 16. This is found by determining the value that completes the square, based on the coefficient of the linear term.
Step-by-step explanation:
To turn the quadratic expression 25x^2-40x+c into a perfect square trinomial, we need to find the value of c that satisfies the condition. A perfect square trinomial is in the form of (ax+b)^2 which equates to a^2x^2 + 2abx + b^2 when expanded. Our goal is to match the given quadratic expression with this form.
In the given expression, the coefficient of x^2 is 25, which is a^2, thus a is 5. To determine the constant term b^2, we look at the linear coefficient, which is -40. The term 2ab should equal -40, meaning 2*5*b equals -40, so b equals -40/(2*5) or -4. Therefore, the value of b^2, which is equal to c, is (-4)^2 = 16.
The value of c that would make 25x^2 - 40x + c a perfect square trinomial is 16.