Question

How do you solve: $-2x^2 + 8 = 0#?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(8)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-2x^2 + 8 - color(red)(8) = 0 - color(red)(8)`

`-2x^2 + 0 = -8`

`-2x^2 = -8`

Next, divide each side of the equation by `color(red)(-2)` to isolate `x^2` while keeping the equation balanced:

`(-2x^2)/color(red)(-2) = (-8)/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))x^2)/cancel(color(red)(-2)) = 4`

`x^2 = 4`

Now, take the square root of each side of the equation to solve for `x` while keeping the equation balanced. Remember, the square root of a number produces both a negative and positive result:

`sqrt(x^2) = sqrt(4)`

`x = +-2`

Answer 2

`x = 2 ,-2`

Explanation:

`-2 x^2 + 8 =0`

subtract `-8` to both sides
`-2 x^2 + 8 - 8=0 -8`
`-2 x^2 = -8`

divide `-23` to both sides
`(-2 x^2) /-2 = -8/-2`
`x^2 = 4`

square root both sides
`sqrt (x^2) = sqrt 4`
`x = +-2`