Solubility of a Substance in solution

[xykiist]

What is the solubility of Mg(OH)₂ in a 0.55mol/L solution of KOH if the Ksp of Mg(OH)₂ is 9.0x10^-12?

I figured out that the initial concentration of OH- in the solution is 0.55mol/L. I did an ICE table for Mg(OH)₂ and (assume x represents an unknown concentration) found that the concentration of Mg2+ is x, and OH- is 0.55mol/L+2x.
So if I continue with it, I get to this point:

Ksp=[Mg2+][OH-]^2
9.0x10^-12=x(2x+0.55)^2
When i expand it and move everything to the right, i get a cubic equation that takes a lot of time to solve and so I get the feeling I'm not approaching this correctly. Any help?

 

[chemisttree]

Since the Ksp of MgOH₂ is only 9X10^-12, you see that the concentration of OH^- is ABSOLUTELY DOMINATED by the concentration of OH^- due to KOH, which is completely soluble at that concentration. Thus, the hydroxide term for your solubility expression is quite accurately approximated as (0.55)².