## Solving the Equation (x+1)^2 - 9 = 0

This equation is a quadratic equation in disguise. We can solve it by following these steps:

### 1. Simplifying the Equation

**Expand the square:**(x+1)^2 = x^2 + 2x + 1**Substitute:**The equation becomes: x^2 + 2x + 1 - 9 = 0**Combine constants:**x^2 + 2x - 8 = 0

### 2. Solving the Quadratic Equation

Now we have a standard quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = 2, and c = -8. We can solve this using various methods:

**a) Factoring:**

**Find two numbers that add up to b (2) and multiply to c (-8).**These numbers are 4 and -2.**Factor the equation:**(x + 4)(x - 2) = 0**Set each factor to zero and solve for x:**- x + 4 = 0 => x = -4
- x - 2 = 0 => x = 2

**b) Quadratic Formula:**

- The quadratic formula solves for x in any equation of the form ax^2 + bx + c = 0:
- x = (-b ± √(b^2 - 4ac)) / 2a

**Substitute the values:**- x = (-2 ± √(2^2 - 4 * 1 * -8)) / 2 * 1
- x = (-2 ± √(36)) / 2
- x = (-2 ± 6) / 2

**Solve for x:**- x = (-2 + 6) / 2 = 2
- x = (-2 - 6) / 2 = -4

### 3. Solution

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