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Question

The quadratic x^2+(2.6)x+3.6 can be written in the form (x+b)^2+c, where b and c are constants. What is b+c (as a decimal)?

Accepted Answer

We complete the square. We have (x+1.3)^2 = x^2 + (2.6)x + 1.69, and so align* x^2+(2.6)x+3.6 &= (x+1.3)^2 - 1.69 + 3.6 &= (x+1.3)^2 + 1.91. align*Therefore, b=1.3 and c=1.91, which gives us b+c = 3.21.