Question

How do you solve `13-8n^2=-1139`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(13)` from each side of the equation to isolate the `n` term while keeping the equation balanced:

`-color(red)(13) + 13 - 8n^2 = -color(red)(13) - 1139`

`0 - 8n^2 = -1152`

`-8n^2 = -1152`

Next, divide each side of the equation by `color(red)(-8)` to isolate `n^2` while keeping the equation balanced:

`(-8n^2)/color(red)(-8) = (-1152)/color(red)(-8)`

`(color(red)(cancel(color(black)(-8)))n^2)/cancel(color(red)(-8)) = 144`

`n^2 = 144`

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 positive and a negative result:

`sqrt(n^2) = +-sqrt(144)`

`n = +-12`