f(x) = -8x^2 + 8x + 7 = 0
8x^2 - 8x - 7 = 0
(ax + b)^2 = (ax)^2 + 2abx + b^2
(x√(8))^2+2(√(8))(-√(8)/2)x+(-√(8)/2)^2-(-√(8)/2)^2-7=0
(x√(8)-√(8)/2)^2 - (-√(8)/2)^2 - 7 = 0
8(x-1/2)^2 - (8/4) - 7 = 0
8(x-1/2)^2 = 9
(x-1/2)^2 = 9/8 = 3*3*2/2*2*2*2
|x-1/2| = 3√(2)/4
x = 1/2 ± 3√(2)/4
The only answer with pairs whose average is 1/2 is A.
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