I have figured out the answer to the question, but I have no idea why and how it works.

I have attached a copy of the question. I do apologize I am still having trouble putting in to latex, I can install some but not all, so bare with me.

So if I multiple out the matrices I get $\chi$2 + 10$\rightarrow$ I then minus this from the quadratic $\chi$2 + 8$\chi$ + 10 = 0 $\rightarrow$ Which then gives me 8$\chi$ = 0

reagrange and I have $\chi$ = -8

Which is the right answer, I checked the mark scheme but I am suppose to find the value of K and not x. This make me think I have done the wrong maths but got the right answer.

Could someone point out if I have gone wrong, it would be very helpful.

It is the one highlighted.

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