Have you have any ideas so far?
The idea is sound, but you've made a mistake or two in carrying it out. Going from
to
you lost the minus sign. You should have gotten
This is a mistake that, due to another sign error, you later correct! This is a bit sloppy.
So, I'd say I agree with your last step, but only as the result of two self-correcting sign errors.
I should also point out that you have done one (what we call) irreversible step, when you squared the equation. Squaring an equation can sometimes introduce spurious results. I think in your case it does. So, when you get your answers, double-check them against your original equation, and make sure they satisfy the original equation. You should always double-check the answers to problems anyway, to make sure they make sense. Make sense?