How do you solve x² + 12x + 5 = 0 using the completing the square method?

To solve the quadratic equation x² + 12x + 5 = 0 by completing the square, follow these steps:

1. Start with the equation:

x² + 12x + 5 = 0

2. Move the constant term to the other side of the equation:

x² + 12x = -5

3. To complete the square, take half of the coefficient of x (which is 12), square it, and add it to both sides:

Half of 12 is 6, and squaring it gives us 36. Now add 36 to both sides:

x² + 12x + 36 = -5 + 36

4. Simplify the equation:

x² + 12x + 36 = 31

5. Now, the left side is a perfect square trinomial:

(x + 6)² = 31

6. Take the square root of both sides:

x + 6 = ±√31

7. Isolate x by subtracting 6 from both sides:

x = -6 ± √31

Therefore, the solutions to the equation x² + 12x + 5 = 0 are:

x = -6 + √31 and x = -6 – √31.