Question

How do you solve `5x ^ { 2} = 65`?

Answer 1

See a solution process below:

Explanation:

First, divide each side of the equation by `color(red)(5)` to isolate `x^2` while keeping the equation balanced:

`(5x^2)/color(red)(5) = 65/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x^2)/cancel(color(red)(5)) = 13`

`x^2 = 13`

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 results in both a negative and positive answer:

`sqrt(x^2) = +-sqrt(13)`

`x = +-sqrt(13)`

`x = +-3.606` rounded to the nearest thousandth.