How do you solve the equation x² + 12x + 11 by completing the square?

To solve the quadratic equation x² + 12x + 11 = 0 by completing the square, follow these steps:

1. Move the constant to the other side:
   Start by isolating the x² and 12x terms:

x² + 12x = -11

2. Complete the square:
   To complete the square, take half of the coefficient of x: 12. Half of 12 is 6. Now, square it (6² = 36) and add that value to both sides of the equation:

x² + 12x + 36 = -11 + 36

3. Rewrite as a square:
   Now the left side can be factored:

(x + 6)² = 25

4. Take the square root of both sides:
   Apply the square root to both sides of the equation:

x + 6 = ±5

5. Solve for x:
   You then have two cases to solve:
• x + 6 = 5
  Subtract 6 from both sides:

x = 5 - 6 = -1

• x + 6 = -5
  Subtract 6 from both sides:

x = -5 - 6 = -11

6. Conclusion:
   The solution set of the equation is:

x = -1, x = -11