# Solve x^{2} - 24x = -80 by completing the square. What is the solution set of the equation?

{2, 40}, {4, 20}, {5, 16}, {8, 10}

**Solution:**

Given equation x^{2} - 24x = -80

Divide the coefficient of the x term by 2 then square the result.

This number will be added to both sides of the equation.

For the quadratic equation x^{2} - 24x = -80, the coefficient of the x term is -24

So (-24/2)^{2} = (-12)^{2} = 144

⇒ x^{2} - 24x +144 = -80 + 144

⇒ x^{2} - 24x + 12^{2 }= -80 + 144

⇒ {x^{2} - 2(x)(12) + 12} = 64 [since a^{2} -2ab +b^{2} = (a-b)^{2}]

⇒ (x - 12)^{2} = 64

⇒ (x - 12)^{2} = (8)^{2}

Applying square root on both sides, we get

⇒ x - 12 = ±8

⇒ x = 12 ± 8

⇒ x = 20, 4

The solution set is {4, 20}

## Solve x^{2} - 24x = -80 by completing the square. What is the solution set of the equation?

**Summary:**

By solving x^{2} - 24x = -80 by completing the square, we get a solution set as {4, 20}.