## Solving the Equation (x - 4)² = 169

This equation is a quadratic equation in disguise. Let's break it down step-by-step to find the solutions for *x*.

**1. Take the Square Root of Both Sides:**

The first step is to get rid of the square on the left-hand side. We do this by taking the square root of both sides of the equation:

√[(x - 4)²] = ±√169

**2. Simplify:**

The square root of (x - 4)² is simply (x - 4). The square root of 169 is 13. Remember that we need to consider both positive and negative roots:

x - 4 = ±13

**3. Isolate x:**

To isolate *x*, we add 4 to both sides of the equation:

x = 4 ± 13

**4. Solve for x:**

Now we have two possible solutions:

**x = 4 + 13 = 17****x = 4 - 13 = -9**

**Therefore, the solutions to the equation (x - 4)² = 169 are x = 17 and x = -9.**

**Key Points:**

- Remember to consider both positive and negative roots when taking the square root of a number.
- Always check your answers by substituting them back into the original equation to ensure they are valid solutions.