The equation is

.
Factoring 2, we get

.
We notice that

, so

.
Substituting in the previous equation, we have:
![y=2(x^2-16x+28)=2[(x-8)^2-64+28]=2[(x-8)^2-36]](https://tex.z-dn.net/?f=y%3D2%28x%5E2-16x%2B28%29%3D2%5B%28x-8%29%5E2-64%2B28%5D%3D2%5B%28x-8%29%5E2-36%5D)
,
distributing 2 over the two terms inside the brackets, we finally get:

This is a parabola opening upwards, since the coefficient of x^2 in the original equation is positive, and whose vertex is (8, -72), which is the lowest point of this parabola.
Answer:

; x-coordinate of the minimum: 8.