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 form for completing the square for the expression \( x^2 + bx \) is:
\[ x^2 + bx = \left( x + \frac{b}{2} \right)^2 - \left( \frac{b}{2} \right)^2 \]
In our case, we have \( b = -8 \). We can find \( \frac{b}{2} \):
\[ \frac{-8}{2} = -4 \]
Next, we calculate \( \left( \frac{b}{2} \right)^2 \):
\[ (-4)^2 = 16 \]
To complete the square, we need to add and subtract this value. Thus, we rewrite the expression:
\[ x^2 - 8x + 16 - 16 + c \]
To make the left-hand side a perfect square trinomial, we set \( c \) such that:
\[ c - 16 = 0 \implies c = 16 \]
Thus, the value of \( c \) that would make the left-hand side a perfect square trinomial is
\[ \boxed{16} \]
Now, the left-hand side becomes:
\[ x^2 - 8x + 16 = (x - 4)^2 \]
So, the revised equation becomes:
\[ (x - 4)^2 = 13 \]