## Solving the Equation: (x+4)^2 - 25 = 0

This equation is a quadratic equation in disguise. We can solve it using a few simple steps:

**1. Simplify using the difference of squares pattern:**

The expression on the left-hand side of the equation is in the form of a difference of squares: **(a^2 - b^2)**, where **a = x+4** and **b = 5**. We can factor this using the formula: **(a + b)(a - b)**.

Applying this to our equation:

**(x + 4 + 5)(x + 4 - 5) = 0**

**2. Simplify the expression:**

**(x + 9)(x - 1) = 0**

**3. Apply the Zero Product Property:**

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.

Therefore, either:

**x + 9 = 0**or**x - 1 = 0**

**4. Solve for x:**

**x + 9 = 0**-->**x = -9****x - 1 = 0**-->**x = 1**

**Therefore, the solutions to the equation (x+4)^2 - 25 = 0 are x = -9 and x = 1.**