## Solving the Equation (x-5)^2 = 100

This equation involves a squared term, making it a quadratic equation. Let's break down how to solve it:

### 1. Taking the Square Root

**Isolate the squared term:**We already have the squared term isolated on one side of the equation.**Take the square root of both sides:**Remember that taking the square root introduces both positive and negative solutions.- √(x-5)² = ±√100
- x - 5 = ±10

### 2. Solving for x

**Separate the equations:**We have two possible equations to solve:- x - 5 = 10
- x - 5 = -10

**Solve for x in each equation:****Equation 1:**x = 10 + 5 = 15**Equation 2:**x = -10 + 5 = -5

### Solutions

Therefore, the solutions to the equation (x-5)² = 100 are **x = 15** and **x = -5**.