Complete the square for the equation x^2 - 12x + 8 = 0

To complete the square, we will need to put the equation into the form (x - a)² - b + 8 = 0, where a is half of the coefficient of x (12 in this case) and b is the value we need to subtract in order for the new form of the equation to be equivalent to the original. To begin we initially get (x - 6)² - b + 8 = 0 since 6 is half of 12. To find b we expand (x-6)² to get x^2 - 12x + 36 so we realize we need to subtract 36. So our equation is (x - 6)² - 36 + 8 = 0 which we can simplify to (x - 6)² - 28 = 0.