The given equation is
x^2 + 12x + 4 = 0
Subtracting 4 from both sides, we have
x^2 + 12x + 4 - 4 = 0 - 4
x^2 + 12x = - 4
To complete the square, the first step is to add the square of half of the coefficient of x to both sides of the equation. From the equation,
coefficient of x = 12
half of the coefficient of x = 12/2 = 6
square of half of the coefficient of x = 6^2
By adding 6^2 to both sides of the equation, we have
x^2 + 12x + 6^2 = - 4 + 6^2
(x + 6)^2 = - 4 + 36
(x + 6)^2 = 32