For example:

There is a passage in BR with a question that says, "The maximum [Ca2+] in a pH=14 solution would be which of the following values?"

They gave a Ksp for Ca(OH)2 at Ksp = 4.3*10^-6 M^3 in the passage

I solved it like this:

Since they gave a pH of 14, I knew the [OH-] was 1 because of 10^-poH

I took that as meaning that the initial concentration of OH- before dissolution of CaOH was 1

So I set up an ICE table

Ca(OH)2--->Ca + 2OH-

-- 0 1

-x +x +2x

So I got an equation: 4.3*10^-6 = x(1 + 2x)^2

Well, first of all, I thought you ignored 2x in this case? If I did that, I would get x^2 = 4.3*10^-6, which doesn't make sense for this problem. Why is this like this in this case?

So I tried to solve it without ignoring 2x, and I got 1*10^-3

In the answer, they solved it like this:

Ksp = [Ca2+][OH-]^2

Then for some reason, they just plugged the 1 M value for [OH-] concentration from the pH to this Ksp expression and got Ksp = [Ca2+]. Using the Ksp value given, they got an answer of 4.3*10^-6 M

So I'm confused because I followed the correct method for solving with an ICE table but I got it wrong. I guess it must be because the ICE table is meant for a different type of problem? I don't see why they just plugged the initial value right into the Ksp expression