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?

x2 −8x + c = 13


(1 point)
Responses

-4
-4

64
64

4
4

-8
-8

16

Answer 1

To determine the value of \( c \) that will make the left-hand side of the equation \( x^2 - 8x + c \) a perfect square trinomial, we can use the formula for completing the square.

1. Start with the quadratic \( x^2 - 8x \).

2. Take the coefficient of \( x \) (which is \(-8\)), divide it by 2, and square it:

   \[ \left( \frac{-8}{2} \right)^2 = (-4)^2 = 16 \]

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

The complete expression becomes:

\[ x^2 - 8x + 16 = (x - 4)^2 \]

Thus, the answer is:

16