assuming that you want to allow colliding accounts/passwords if the user is dumb enough to to use "sex" as his password...

why do you need x at all?

I think x is simply a kind of salt (which does need to be remembered, by you (really not a salt but second half of the password) or the computer (fixed location computer salt))

your prescription for finding x is deterministic as a function of password. In effect, you are just applying a croocked form of SHA256.
Occams razor, if it does not add security leave it behind, and simply use SHA256(password) if you really want the same passwords to generate the same accounts...