You notice that the following quadratic equation cannot be factored, so you solve it by completing the square.

Question

What value of c would make the left-hand side of this equation a perfect square trinomial?

x^2 − 8x + c = 13


(1 point)
Responses

-8
-8

64
64

16
16

4
4

-4

Answer 1

To make the left-hand side of the equation \( x^2 - 8x + c \) a perfect square trinomial, we need to complete the square.

The general approach for completing the square is to take the coefficient of \( x \) (which is -8 in this case), divide it by 2, and then square the result.

1. Take the coefficient of \( x \): \(-8\)
2. Divide it by 2: \(-8 / 2 = -4\)
3. Square the result: \((-4)^2 = 16\)

So, the value of \( c \) that would make \( x^2 - 8x + c \) a perfect square trinomial is \( 16 \).

Thus, the answer is \( \boxed{16} \).