solve using perfect squre factoring patterns x^2-8+16=25

I assume you mean (x^2) - 8x +16 = 25

(x^2) - 8x +16 = (x^2) - 4x - 4x + 16

= x(x-4) -4(x-4)

= (x-4)^2 = 25

taking square root of both sides

(x-4) = +/- 5 => x = 1 or x = -9

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