Question

How do you solve `-10n^2-10=470`?

Answer 1

`n=+-4isqrt3`

Explanation:

If we start with `-10n^2-10=470`, our first step is to isolate the variable (`n`). To do that, we add `10` to both sides, giving us: `-10n^2=480`. If we divide by -10 on both sides we get n^2=-48. We want to solve for `n`, not `n^2`, so we need to "undo" the square by square-rooting it. What we do on one side, we must do to the other side, so we have `sqrt(n^2)=+-sqrt(-48)` or `n=+-sqrt(-48)`.

We can rewrite `sqrt(-48)` as `sqrt(-1)*sqrt(48)`. `sqrt(-1)` is `i`, and `sqrt48` can be simplified to `4sqrt3`.

Putting it all together, we get `n=+-4isqrt3`