x²- 12x + 11 = 0
subtract 11 from both-side
x² - 12x = -11
Add square of half of the coefficient of x to both-side
x² - 12x + (-6)² = -11 + (-6)²
(x- 6)² = -11 + 36
(x-6)² =25
Take the square root of both-side
x - 6 = ±5
add 6 to both-side
x = ±5 + 6
Either x = 5 + 6 or x = -5+6
x = 11 or x = 1