## Solving the Equation (x+6)^2 - 25 = 0

This equation is a quadratic equation in disguise. Let's break down how to solve it:

### 1. Simplify the Equation

We can simplify the equation by using the difference of squares factorization:

**(a² - b²) = (a + b)(a - b)**

Applying this to our equation, we get:

**(x + 6)² - 25 = 0****[(x + 6) + 5][(x + 6) - 5] = 0****(x + 11)(x + 1) = 0**

### 2. Solve for x

Now we have a simple product of two factors equaling zero. This means at least one of the factors must be zero. So we have two possible solutions:

**x + 11 = 0****x + 1 = 0**

Solving for x in each case:

**x = -11****x = -1**

### 3. Solution

Therefore, the solutions to the equation (x + 6)² - 25 = 0 are **x = -11** and **x = -1**.

### Conclusion

By simplifying the equation and using the difference of squares factorization, we were able to solve the quadratic equation (x + 6)² - 25 = 0 and find its two solutions.