Question

Find the solution to the following equation by transforming it into a perfect square trinomial. x2 – 12x = 64

A) {–4, 16}
B) {–15, 25}
C) {–20, 30}
D) {59, 69}

Answer 1

`x^2-12x=64\\\\x^2-2\cdot6\cdot x=64\\\\(x^2-2\cdot6\cdot x+6^2)-6^2=64\\\\(x-6)^2-36=64\\\\(x-6)^2=64+36\\\\(x-6)^2=100\qquad|√((\ldots))\\\\\\x-6=-10\qquad\vee\qquad x-6=10\\\\x=-10+6\qquad\vee\qquad x=10+6\\\\\boxed{x=-4\qquad\vee\qquad x=16}`

Answer A)