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Question

The quadratic x^2-20x+36 can be written in the form (x+b)^2+c, where b and c are constants. What is b+c?

Accepted Answer

We complete the square. We have (x-10)^2 = x^2 - 20x + 100, and so align* x^2-20x+ 36 &= (x-10)^2 + (36-100) &= (x-10)^2 - 64. align*Therefore, b=-10 and c=-64, which gives us b+c = -74.