Solve x² - 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 x² - 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 x² - 24x = -80, the coefficient of the x term is -24

So (-24/2)² = (-12)² = 144

⇒ x² - 24x +144 = -80 + 144

⇒ x² - 24x + 12² = -80 + 144

⇒ {x² - 2(x)(12) + 12} = 64 [since a² -2ab +b² = (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}

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Solve x² - 24x = -80 by completing the square. What is the solution set of the equation?

Summary:

By solving x² - 24x = -80 by completing the square, we get a solution set as {4, 20}.