Help help help is needed

I need the solve with process for this problem. please help

Given that, x^x^x^x^… =2
Taking log₂ in both sides,we get-
log₂x^x^x^x^x…= log₂2
or, x^x^x^… × log₂x =1
or, 2 × log₂x=1 [as x^x^x^x^… =2]
or, log₂x=1/2
or, x=2^1/2
so,x is equal to ±√2

the sum of all the possible values of x is √2+(-√2)

Hence,we get that, the answer is √2+(-√2) = 0