Question

How do you solve the equation `2/3x^2-4=12`?

Answer 1

The answer is `x=+-2sqrt6`.
.

Explanation:

Solve:

`2/3x^2-4=12`

Add `4` to both sides.

`2/3x^2-color(red)cancel(color(black)(4))+color(red)cancel(color(black)(4))=12+4`

Simplify.

`2/3x^2=16`

Multiply both sides by `3`.

`color(red)cancel(color(black)(3))xx2/color(red)cancel(color(black)(3))x^2=16xx3`

Simplify.

`2x^2=48`

Divide both sides by `2`.

`color(red)cancel(color(black)(2))/color(red)cancel(color(black)(2))x^2=48/2`

Simplify.

`x^2=24`

Take the square root of both sides.

`sqrt(x^2)=+-sqrt24`

Simplify.

`x=+-sqrt24`

Simplify `sqrt24` using prime factorization.

`x=+-sqrt(2xx2xx2xx3)`

`x=+-sqrt(2^2xx2xx3)`

`x=+-2sqrt6`