>But I fail to see how this would make a significant
>difference in the outcome, since for the negative root you
>would simply end up getting -a=-b which is the same as
>saying a=b, maybe I'm missing something here too, I'm not
>sure.

There is another possibility here: a = -b.

For example,

(-5)2 = 25 = 52,

but you would not claim that -5 = 5, right?