Question

How do you solve `6x^2=1296`?

Answer 1

See a solution process below:

Explanation:

First, divide each side of the equation by `color(red)(6)` to isolate the `x` term while keeping the equation balanced:

`(6x^2)/color(red)(6) = 1296/color(red)(6)`

`(color(red)(cancel(color(black)(6)))x^2)/cancel(color(red)(6)) = 216`

`x^2 = 216`

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

`sqrt(x^2) = +-sqrt(216)`

`x = +-sqrt(36 * 6)`

`x = +-sqrt(36)sqrt(6)`

`x = +-6sqrt(6)`

The Solution Set is: `x = {-6sqrt(6), 6sqrt(6)}`