I was doing these questions, and did them all up to question (e), but then I got stuck. I looked at the mark scheme but still don't understand it.

Please could someone explain the steps to me?

Here's the mark scheme:

So I understand everything up to the quadratic equations - it's the manipulating from there that I don't understand.

How does 20 become 4.5, when 32 becomes 4.8? What did they multiply by?

I don't understand the $\displaystyle cos\frac{\pi}{10}$ line onwards. 'since max value of cosine => angle closest to zero' - is this because pi by 10 is the closest value to 0 that is a solution?

Why not simplify the $\displaystyle \sqrt{400-4(16)(5)$?

How do you know that's the value of $\displaystyle cos\frac{7\pi}{10}$?

I realise that this is a long post and that I have a lot of questions, but help with this question will be greatly appreciated.