# What number that needs to be added to both sides of the equation x^2 + 4x = 96 to complete the square?

Dec 15, 2015

The number to be added to both sides is 4.

#### Explanation:

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 ${x}^{2} + 4 x = 96$, the coefficient of the $x$ term is $4$. So ${\left(\frac{4}{2}\right)}^{2} = 4$.

${x}^{2} + 4 x + 4 = 96 + 4$

${x}^{2} + 4 x + 4 = 100$

${\left(x + 2\right)}^{2} = 100$

Take the square root of both sides.

$x + 2 = \pm 10$

Subtract $2$ from both sides.

$x = - 2 \pm 10$

Solve for $x$.

$x = - 2 + 10 = 8$

$x = - 2 - 10 = - 12$

$x = 8 , - 12$