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

To make the left-hand side of the equation \( x^2 - 8x + c = 13 \) a perfect square trinomial, we can use the following formula for completing the square:

For a quadratic in the form \( x^2 + bx \), we can find the value of \( c \) using the formula:

\[
c = \left( \frac{b}{2} \right)^2
\]

In this case, \( b = -8 \). So we calculate:

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

Thus, the value of \( c \) that would make the left-hand side of the equation a perfect square trinomial is \( 16 \).

The correct response is:
**16**.