Question

Solve x2 + 14x = −24 by completing the square. What is the solution set of the equation?

Answer 1

$x^2 + 14x = -24$

In completing the square , we take half of coefficient of middle term x and then square it. Then we add it on both sides of the equation

Here coefficient of middle term x is +14

Half of 14 = $\frac{14}{2} = 7$

square it , so $7^2 = 49$

Now add 49 on both sides

$x^2 + 14x + 49 = -24 + 49$

$(x+7)(x+7)= 25$

$(x+7)^2=25$

Take square root on both sides

x + 7 = + - 5

Now make two equations

x+7 = 5 and x+7 = -5

Solve for x by subtracting 7 on both sides

x = -2  and x= -12

Solution set is {-12, -2}

Answer 2

X^2 + 14x = -24
x^2 + 14x + 24 = 0
x^2 + 12x + 2x + 24 = 0
x (x + 12) + 2 (x + 12) = 0
(x + 12) (x + 2) = 0

x + 12 = 0                x + 2 = 0
x = -12                        x = -2