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x^2 + 8x - 4 = 0
(x^2 + 8x + 8/2^2) - 4 - 8/2^2 = 0
(x^2 + 8x + 16) - 4 - 16 = 0
(x^2 + 8x + 16) - 20 = 0
(x + 4)(x + 4) - 20 = 0
The number that is to be added to complete the square is 8/2^2, or 16.