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To determine the value of \( c \) that would make the left-hand side of the equation \( x^2 - 8x + c = 13 \) a perfect square trinomial, we use the method of completing the square.
The expression \( x^2 - 8x \) can be transformed into a perfect square by following these steps:
1. Take the coefficient of \( x \), which is \(-8\).
2. Divide it by 2: \(-8 \div 2 = -4\).
3. Square the result: \((-4)^2 = 16\).
Thus, to make \( x^2 - 8x + c \) a perfect square trinomial, we set \( c = 16 \).
So the required value of \( c \) is **16**.