First, we want to set the equation equal to zero and
bring the constant to the other side of the equal sign

x² - 12x + 11 = 0

x² - 12x + ____ = -11


Next, divide the middle term by 2 and then square it

12 / 2

= 6          6² = 36

Add the squared value to both sides

x² - 12x + 36 = -11 + 36

x² - 12x + 36 = 25


Factor the perfect square you have created on the left side

(x - 6)² = 25


and finally, solve for x

(x - 6)² = 25

√ (x - 6)² = ±√ 25

x - 6 = ± 5

x = ± 5 + 6

x₁ = 5 + 6 = 11
x₂ = - 5 + 6 = 1