Question

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

Answer 1

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+4x=96`, the coefficient of the `x` term is `4`. So `(4/2)^2=4`.

`x^2+4x+4=96+4`

`x^2+4x+4=100`

`(x+2)^2=100`

Take the square root of both sides.

`x+2=+-10`

Subtract `2` from both sides.

`x=-2+-10`

Solve for `x`.

`x=-2+10=8`

`x=-2-10=-12`

`x=8, -12`