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Question

Jill is trying to solve the following quadratic equation by completing the square: x^2 - 8x - 49 = 0.She rewrites this equation in the form of (ax + b)^2 + c, where a, b, and c are integers. What is ab?

Accepted Answer

We know that (ax + b)^2 + c = (a^2)x^2 + (2ab)x + b^2 + c, meaning that if this to equal x^2 - 8x - 49, we start with a^2 = 1, and so we let a = 1. Then, 2ab = -8, so b = -4. We do not need to find c in this case, so our answer is ab = -4. Note: Letting a = -1 gives us (-x+4)^2 + c, which gives us the same answer.