Solve x² – 24x + 80 by Completing the Square: What is the Solution Set of the Equation?

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

1. Move the constant to the other side: Start with the original equation:
2. x² – 24x = -80
3. Complete the square: Take the coefficient of x, which is -24, divide by 2 to get -12, and then square it to get 144:
4. Add and subtract 144: This means:
5. x² – 24x + 144 = 144 – 80
6. Rearranging gives us:
7. (x – 12)² = 64

Next, we take the square root of both sides:

1. x – 12 = ±8

This results in two equations:

1. x – 12 = 8 → x = 20
2. x – 12 = -8 → x = 4

Thus, the solution set of the equation is:

• x = 20
• x = 4

In conclusion, the solution set of the equation x² – 24x + 80 = 0 is {4, 20}.