## Solving the Equation: (x+3)^2 = (x+8)^2

This equation presents a straightforward algebraic challenge that can be solved using a few basic steps. Let's break it down:

### Expanding the Equation

First, we need to expand the squares on both sides of the equation using the formula (a+b)^2 = a^2 + 2ab + b^2. This gives us:

x^2 + 6x + 9 = x^2 + 16x + 64

### Simplifying the Equation

Next, we can simplify the equation by subtracting x^2 from both sides:

6x + 9 = 16x + 64

Then, subtract 6x from both sides:

9 = 10x + 64

### Isolating the Variable

Finally, subtract 64 from both sides to isolate the variable:

-55 = 10x

And divide both sides by 10:

x = -5.5

### Solution

Therefore, the solution to the equation (x+3)^2 = (x+8)^2 is **x = -5.5**.

### Conclusion

This equation demonstrates how to solve a quadratic equation by expanding, simplifying, and isolating the variable. The key is to remember the basic algebraic rules and apply them systematically.