## Solving the Equation (x – 5)2 = 17

This equation involves a squared term and a constant, making it a quadratic equation. Here's how to solve for the values of x:

### 1. Isolate the Squared Term

Begin by taking the square root of both sides of the equation:

√[(x – 5)2] = ±√17

This gives us:

x – 5 = ±√17

### 2. Solve for x

Now, isolate x by adding 5 to both sides:

x = 5 ±√17

### 3. Finding the Solutions

Therefore, the solutions to the equation (x – 5)2 = 17 are:

**x = 5 + √17****x = 5 – √17**

These are the two distinct values of x that satisfy the original equation.

### Understanding the Result

This equation represents a parabola with its vertex at (5, 0). The solutions we found are the x-coordinates where the parabola intersects the horizontal line y = √17.