Diverse Ion effect and Activity coefficients problem

[higherme]

The question:

How many grams of Ba(IO3)2 can be dissolved in 700mL of a 0.100M KIO3 solution at 25C? use activity coefficients for this. (Ksp of Ba(IO3)2 =1.57E-9)

my answer:

I used this equation: Ksp = (concentration) * (activity coefficient)

well i found out that my ionic strength of KIO3 is 0.100M and from a chart, i found the respective activity coeff for Ba2+ and IO3-.
Ba2+ ---> 0.38
IO3^- ----> 0.775

Ba(IO3)2 <----> Ba2+ + 2IO3^-
I 0 x 0.100M
C +x +2x
E x 0.100M+2x


using the equation above,
Ksp = [Ba2+]*(activity coeff of Ba) * [IO3^-]^2 * (activity coeff of IO3^-)^2
1.57E-9 = (x)(0.38) * (0.100+2x)^2 * (0.775)^2

so i solve for X and that would be the concentration of Ba(IO3)2 in mol/L

BUT, to solve for X, i found it complicated because there would be 3 solutions for X aren't there?? since it's X^3... so i am confused on what to do.

help appreciated, Thanks.

 

[higherme]

there above numbers below the balanced equation is supposed to be an ICE table