\(x^2 + 14x = -24\)
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}
