1-sqrt(x) = sqrt(1-x)

1-sqrt(x) = sqrt(1-x)      first, square both sides

1 - 2√x + x  = 1 - x        subtract 1 from both sides

x - 2√x  =  - x                rearrange

2x    = 2√x                    divide by 2 on both sides

x  = √x                          square both sides again

x^2  = x                        subtract x from both sides

x^2 - x  = 0                   factor

x ( x - 1)  = 0                  and setting each factor to  0, we have that x = 0 and x =1

Both of these solutions "work" in the original problem