Given x = sqrt(-x), I get the result x = 0.
However, x could also be -1. Explicitly entering -1 = root(1) comes up false.
Yet given root(1), I get 1 and -1 as expected
It appears that only the principle root is being considered here. Perhaps this is the root (no pun intended) cause of the original issue?
Would you agree that -1 should appear by default, rather than having to know this extra syntax?
we can give WolframAlpha a helping hand: