The least possible value How to find the least possible value for :$$(x-1)^2+(x-2)^2+(x-3)^2+(x-4)^2+(x-5)^2$$
For every real $x$

Hint:
$(x-1)^2+(x-2)^2+(x-3)^2+(x-4)^2+(x-5)^2 \ge 0$
$5x^2+1+4+9+16+25 \ge 15x$
$5x^2 +55 -15x \ge 0 \implies x^2+11-3x \ge 0$
Aliter: $(x-3)=k$
You get 
$(k+2)^2+(k+1)^2+(k)^2+(k-1)^2+(k-2)^2 \ge 0$
$k^2+11 \ge 0$
