Write x^2 + 8x + 7 in the form (x + a)^2 + b
We work from right to left (x + a)2 = x2 + 2ax + a2 2a = 8 [coefficients of x must match] a = 4 (x + 4)2 = x2 + 8x + 16 [substitute in a = 4] x2 + 8x + 16 + b = x2 + 8x + 7 [equate sides and solve for b] b = -9 Giving us the expression: x2 + 8x + 7 = (x + 4)2 - 9
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