Solving the quadratic equation x² + 12x + 6 = 0 by using the completing-the-square method, x = - 6 ± √30
To solve x² + 12x + 6 = 0 by using the completing-the-square method, we proceed as follows.
Since we have the quadratic equation x² + 12x + 6 = 0, to solve by completing the square, we rewrite the equation as
x² + 12x + 6 = 0
x² + 12x = - 6
Next, we add the square of half the coefficient of x to both sides. So, we have that
x² + 12x + (12/2)² = - 6 + (12/2)²
x² + 12x + 6² = - 6 + 6²
(x + 6)² = - 6 + 36
(x + 6)² = 30
Now, taking the square root of both sides, we have that
(x + 6)² = 30
√(x + 6)² = ±√30
x + 6 = ±√30
x = - 6 ± √30
So, the value of x = - 6 ± √30.