Question 388773
what you did so far is correct, but you did not finish the problem

continuing from where you ended,

(x-2)^2=-2
(x-2 = + or -sqrt (-2)
x = 2 + or -sqrt (-2)
at this point you can see there is no real  number solution because the sqrt of a negative number is imaginary.

to compete the problem,
x =2 + or -sqrt (2)*sqrt(-1)
sqrt(-1) = i

ans: 

x=2 + or -sqrt (2)i
 This problem has 2 imaginary number solutions