## Solving the Equation (x - 5)² + 7 = 2x

This article will guide you through solving the quadratic equation (x - 5)² + 7 = 2x. We'll use algebraic manipulation to find the solutions for 'x'.

### 1. Expanding the Equation

First, we need to expand the equation by getting rid of the squared term.

(x - 5)² = (x - 5)(x - 5) = x² - 10x + 25

Now our equation becomes:

x² - 10x + 25 + 7 = 2x

### 2. Simplifying the Equation

Next, we will simplify the equation by combining like terms and moving all terms to one side:

x² - 10x - 2x + 25 + 7 = 0 x² - 12x + 32 = 0

### 3. Factoring the Equation

Now, we can factor the quadratic equation:

(x - 8)(x - 4) = 0

### 4. Solving for x

Finally, we can solve for x by setting each factor equal to zero:

x - 8 = 0 or x - 4 = 0

Solving for x, we get:

x = 8 or x = 4

### Conclusion

Therefore, the solutions to the equation (x - 5)² + 7 = 2x are **x = 8** and **x = 4**.