Mean value by Least Squares Method

[Hans Wurst]

The mean is the average of the numbers or in other words \(\bar{x} = \displaystyle \frac{1}{n}\displaystyle\sum_{k=1}^{n}x_k\)
How may I derive this simple formula using the Least Squares Method on an HP Prime?
I get quite close to it
\(\displaystyle \frac{\partial \displaystyle \sum_{k=1}^{n}(x(k)-m)^2}{\partial m} = sum(-2*(x(k)-m),k,1,n)\)
alas neither FNROOT nor solve are of much help for the last algebraic step. What do I wrong?

Another problem I was not able yet to solve on an HP Prime: How to prove which of the roots of a quadratic equation is the correct one. It's about orthogonal linear regression (sorry for the link to Wikipedia in german, but I could not find similar in English -- but honestly, the formulas are international), the Least Squares Method is applied to find both coefficients, where for m there are two solutions. One may be eliminated by fiddling out the sign of the third second derivative at the roots (or one root at least). I did so using Reduce, but all I tried so far on a Prime failed.

So in both cases it is not about the result, I'd like to know how to get there using a Prime.

TIA
Hans