I would just like to point out that u2 = 1 - x is not a clear-cut definition of the value of u.
That particular solution suggests that (u2)1/2 = u, when in actuality, (u2)1/2 = |u|.
Hence, there are 2 cases:
If u > 0, |u| = u, and (u2)1/2 = u.
If u < 0, |u| = -u, and (u2)1/2 = -u.