How do you solve x² + 12x + 6 = 0 using the completing the square method?

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

1. Move the constant to the other side: Start by isolating the constant term on one side of the equation. We rewrite the equation as:
   
   x² + 12x = -6
2. Complete the square: To complete the square for the expression on the left side, take half of the coefficient of x (which is 12), square it, and add to both sides of the equation. Half of 12 is 6, and squaring it gives 36:
   
   x² + 12x + 36 = -6 + 36
3. Simplify: Now simplify the equation:
   
   x² + 12x + 36 = 30
4. Rewrite as a perfect square: The left side of the equation can be factored as:
   
   (x + 6)² = 30
5. Take the square root of both sides: Now take the square root of both sides, remembering to consider both the positive and negative roots:
   
   x + 6 = ±√30
6. Solve for x: Finally, isolate x by subtracting 6 from both sides:
   
   x = -6 ± √30

This gives us the two possible solutions for x:

• x = -6 + √30
• x = -6 – √30

Therefore, the solutions to the equation x² + 12x + 6 = 0 using the completing the square method are x = -6 + √30 and x = -6 – √30.