BPT Optimal Portfolio Construction

I am referring to Example 3 on Page 40 of the CFAI Book in Reading 7.

How does one go about constructing this BPT Optimal Portfolio? The CFAI authors seem to have magically found a way to get numbers such as 1,568,627 and 431,373 which I have not been able to decipher.

Can we be asked to construct such a portfolio on the exam? How do we go about doing so? Thanks in advance guys.

1.01X (1st layer) + (2-X) 0.5 (3rd layer) = 1.8

solve for X => 1.568627

and 2-X = 0.431373