You notice that the following quadratic equation cannot be factored, so you solve it by completing the square. What value of c would make the left hand side of this equation a perfect square trinomial? X^2 - 8x + c = 13

To convert the left-hand side of the equation \( x^2 - 8x + c = 13 \) into a perfect square trinomial, we need to determine the value of \( c \) that completes the square.

A quadratic expression of the form \( x^2 - bx \) can be written as a perfect square by using the formula:

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

In this case, \( b = 8 \). Now we calculate \( \left( \frac{8}{2} \right)^2 \):

\[
\frac{8}{2} = 4
\]
\[
4^2 = 16
\]

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

Thus, the answer is:

\[
\boxed{16}
\]