[Slavvo]

Hello everyone,

I have an exam in a few days and i was studying by going through previous year exams. I stumbled upon this one exercise that had the teacher's correction attached to it, and i have been struggling to understand it for the past hour and a half. 
I apologize in advance as the exercise is in french but there is only one relevant sentence here which is the one in blue and it translates to : "Solving the equation gives us"

I am struggling to understand how she goes from the X/(1-2x)^2 = 8.14e99 form, to the X^2-22.4X+5.6=0 form. I tried doing the exercise by turning the K constant into an "a" factor and solving the quadratic equation along with that, but the result it gave me was X=0.25 at the end which does not seem correct. And even after trying my best in every way i can imagine, i simply can't seem to find the same equation, and subsequently, the same answer as her.
 Is her correction just plain wrong ? ( that could be a possibility as she has probably given us more misleading corrections this year than correct ones) Or am i missing something obvious here ?


Many thanks in advance for any potential help or answers !

[Borek]

Nothing makes sense to me. Not only I have no idea where the equation comes from, but also 0.5 is not a solution and it doesn't survive the sanity check - plugging [H₃⁺] = 0 into the equilibrium formula defined in the first line produces not 10⁹⁹, but division by zero.

That also means there are several other things wrong here (pH and pOH are undefined, Kw is ignored, zero concentration can't be part of an equilibrium).

Seems completely off to me.

[Corribus]

It would be helpful to know what the original problem was.

[mjc123]

I don't know where that value of K comes from, but it's nonsense (as is the quadratic equation). It is clear that
K = K_sp/K_w²
I find different values for K_sp, all around 10^-11, so K is of the order of 10¹⁷.
If you make the substitution [H₃O⁺] = δ, and [Mg²⁺] = 0.5 - δ/2 ≈ 0.5 if δ is very small, then you get a simple equation for δ.