# Solve x^{2} + 14x = -24 by completing the square. What is the solution set of the equation?

{-12, -2}, {-7, 7}, {-6, -4} , {-5, 5}

**Solution:**

Given equation x^{2} + 14x = -24

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} + 14x = -24, the coefficient of the x term is 14

So (14/2)^{2} = 49

x^{2} + 14x + 49 = -24 + 49

{x + 7}^{2 }= 25 [ since a^{2} + 2ab + b^{2} = (a+ b)^{2}]

(x + 7)^{2} = 5^{2}

Applying square root on both sides, we get

(x + 7) = ± 5

x = 5 - 7, -5 - 7

x = -2, -12

The solution set for the given equation is {-12, -2}.

## Solve x^{2} + 14x = -24 by completing the square. What is the solution set of the equation?

**Summary:**

By solving by completing the square of the given equation x^{2} + 14x = -24, we get a solution set as {-12, -2}.

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