To solve x^2 - 12x + 8 = 0 by completing the square, we can follow these steps:
Move the constant term to the right side:
x^2 - 12x = -8
Take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 - 12x + (-12/2)^2 = -8 + (-12/2)^2
Simplifying the right side:
x^2 - 12x + 36 = -8 + 36
Factor the left side:
(x - 6)^2 = 28
Take the square root of both sides:
x - 6 = ±√28
Add 6 to both sides:
x = 6 ±√28
Simplify the roots:
x = 6 ±2√7
Therefore, the solutions to the equation x^2 - 12x + 8 = 0 by completing the square are x = 6 + 2√7 and x = 6 - 2√7.