[tex] x^2 + 14x = -24 [/tex]
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 = [tex] \frac{14}{2} = 7[/tex]
square it , so [tex]7^2 = 49[/tex]
Now add 49 on both sides
[tex] x^2 + 14x + 49 = -24 + 49 [/tex]
[tex](x+7)(x+7)= 25 [/tex]
[tex] (x+7)^2=25 [/tex]
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}
