Solve x² + 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 x² + 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 x² + 14x = -24, the coefficient of the x term is 14

So (14/2)² = 49

x² + 14x + 49 = -24 + 49

{x + 7}² = 25 [ since a² + 2ab + b² = (a+ b)²]

(x + 7)² = 5²

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 x² + 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 x² + 14x = -24, we get a solution set as {-12, -2}.