Question

How do I solve `(x-2)^2 = -3` using the square root property?

Answer 1

`x= 2+-(sqrt(3))i`

Explanation:

If `a^2 = b`
then `a = +-sqrt(b)`

In this case `a = (x-2)` and `b = -3`
So
`color(white)("XXXX")x-2 = +-sqrt(-3)`

Note that `sqrt(-3) = sqrt(3)*sqrt(-1)`
and there is no Real value `= sqrt(-1)`.
However, if we are allowed to use Complex values
by definition `i =sqrt(-1)`

Therefore, we can write
`color(white)("XXXX")x-2 =+- (sqrt(3))i`
and after adding 2 to both sides
`color(white)("XXXX")x = 2+-(sqrt(3))i`