What is the equation obtained by completing the square for the expression x² + 6x + 9 = 0?

To complete the square for the quadratic equation x² + 6x + 9 = 0, follow these steps:

1. Start with the equation: x² + 6x + 9 = 0.
2. Notice that the expression on the left side can be expressed as a perfect square. The expression x² + 6x + 9 can be factored.
3. The term 9 is the square of half the coefficient of x, which is 3. Thus, you can rewrite the equation as:
4. (x + 3)² = 0
5. Now we have successfully completed the square. The equation (x + 3)² = 0 implies that x + 3 = 0, leading us to the solution:
6. x = -3

In conclusion, the equation obtained by completing the square for x² + 6x + 9 = 0 is:

(x + 3)² = 0