## Solving the Equation: (x+4)² - (x-5)² = 9

This equation involves simplifying and solving for the variable 'x'. Here's a step-by-step solution:

### 1. Expanding the Squares

We begin by expanding the squares using the formula: **(a+b)² = a² + 2ab + b²** and **(a-b)² = a² - 2ab + b²**

Applying this to our equation:

- (x + 4)² = x² + 8x + 16
- (x - 5)² = x² - 10x + 25

Now our equation becomes:
**x² + 8x + 16 - (x² - 10x + 25) = 9**

### 2. Simplifying the Equation

Let's distribute the negative sign and combine like terms:

x² + 8x + 16 - x² + 10x - 25 = 9 18x - 9 = 9

### 3. Solving for x

Now we have a simple linear equation. Let's isolate 'x':

18x = 9 + 9
18x = 18
x = 18/18
**x = 1**

### Conclusion

Therefore, the solution to the equation (x+4)² - (x-5)² = 9 is **x = 1**.