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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**.