Question

How do you solve `2n^2 = -144`?

Answer 1

`n = ± 6isqrt{2}`

Explanation:

`2n^2 = -144`

`n^2 = -72`

`n = ± sqrt{-72}`

The square root of a negative number will always involve complex numbers.

`n = ± isqrt{72}`

Since `72 / 6^2 = 2`

`n = ± 6isqrt{2}`

Answer 2

`n=+-6sqrt2i`

Explanation:

`"divide both sides by 2"`

`rArrn^2=-144/2=-72`

`color(blue)"take the square root of both sides"`

`rArrn=+-sqrt-72larrcolor(blue)"note plus or minus"`

`[sqrt-72=sqrt(36xx2xx-1)=sqrt36xxsqrt2xxsqrt(-1)]`

`rArrn=+-6sqrt2i`