Minimum value

differentiating with respect to x (using chain rule) gets:

$2(x+12)+2(x+7)+2(x+3)+2(x-14)+2(x-8)\\ =2(5x)\\ =10x$

There is only 1 critical point $x = 0$, and since this function is concave up (the double derivative is positive), it is a minimum point. Plug in zero to your equation to get your answer.

Here's another way, without using calculus:

Expand it to $5x^2 + 462$

Now, the minimum value occurs when $x = 0$, because $x^2$ is always non-negative.