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? x2 −8x + c = 13 (1 point) Responses -4 -4 -8 -8 64 64 16 16 4

Answer 1

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.