Solve algebraically and check your potential solutions: sqrt((x+2) -x =0

Answer 1

√x+2 - x = 0
√x+2 = x
x+2 = x^2
x^2 - x - 2 = 0
(x-2)(x+1) = 0

check for validity

√(2+2) - 2 = 2-2 = 0 ok
√(-1+2) - (-1) = 1 - (-1) = 2 nope

Note that if you had taken the minus √, it would have been ok. But √4 does not mean ±2 - it's just 2.