How can I solve the equation x² + 12x + 6 = 0 using the method of completing the square?

To solve the quadratic equation x² + 12x + 6 = 0 using the method of completing the square, we will follow these steps:

1. Move the constant to the other side: Start by isolating the x terms. We can do this by subtracting 6 from both sides:
2. x² + 12x = -6
3. Complete the square: To complete the square, we take the coefficient of x (which is 12), divide it by 2, and square it:
4. Half of 12 is 6, and 6² = 36.
5. Now, add and subtract this square value inside the equation to keep it balanced:
6. x² + 12x + 36 - 36 = -6
7. This simplifies to:
8. (x + 6)² - 36 = -6
9. Now, add 36 to both sides:
10. (x + 6)² = 30

Now, take the square root of both sides:

• x + 6 = ±√30

Next, isolate x by subtracting 6 from both sides:

• x = -6 ± √30

Final Solutions:

Therefore, the solutions to the equation are:

• x = -6 + √30
• x = -6 - √30

In conclusion, the values of x that satisfy the equation x² + 12x + 6 = 0 are x = -6 + √30 and x = -6 - √30.