FF,
Yup, I think we have narrowed down what I meant - and as said before, none of it was criticising your solution, just querying it being the 'only' one.
I must say my initial reaction to your comment on 'convention' of positive only was 'I've never heard that'. And I was gobsmacked to find it written in the revision notes for A level maths - clearly UK, and one of the maths exams I sat way back when, so how did I miss this convention.
Then I thought about it some more. Whenever I used a square root in physics, it was automatically the positive. When I used it in solving problems around eg angular momentum or geometrical questions, it was automatically the positive. But in algebra and calculus, I don't think it was, and I know I did roots of negative numbers and for some reason I associate them with quadratic equations. So I guess I had some awareness of this rule as applying to 'real life', but was also subliminally driven by the quadratic to thinking on a more theoretical mathematical plane.
I've learnt something about my assumptions. Thank you!
