My algebra is rusty:

I'm solving for x in the following equation:

(x)^(1/2) + (x-(1-x)^(1/2))^(1/2) = 1

After several steps (in some of which I square both sides of the equality), I end up with the equality

x(25x-16) = 0

At this point I'm afraid to eliminate either term of the product in fear of dividing by 0. So I solve for x. I get x=16/25 , 0.

Maple says the only solution is x = 16/25.

Am I supposed to solve this way, but then check the solutions with the original equation in order to compensate for any misleading algebra brought on by me multiplying both sides by a variable?