How can I solve the equation x² - 24x + 80 by completing the square, and what is the solution set?

Solving the Equation x² – 24x + 80 by Completing the Square

To solve the quadratic equation x² – 24x + 80 = 0 by completing the square, follow these steps:

Rearrange the equation: Start with the original equation:
```
x² - 24x + 80 = 0
```
Move the constant term (80) to the other side:
```
x² - 24x = -80
```
Determine the value to complete the square: Take half of the coefficient of x (which is -24), square it, and add it to both sides:
```
                Half of -24 is -12.
                Squaring -12 gives 144.
            
```

Add 144 to both sides:

x² - 24x + 144 = -80 + 144

This simplifies to:

x² - 24x + 144 = 64

Factor the left-hand side:
```
(x - 12)² = 64
```
Take the square root of both sides:
```
x - 12 = ±8
```
Solve for x:
- For x – 12 = 8:
```
x = 8 + 12 = 20
```
- For x – 12 = -8:
```
x = -8 + 12 = 4
```

The solution set of the equation x² – 24x + 80 = 0 is:

{4, 20}