For all real numbers x find the minimum value of
(x + 12)^2 + (x + 7)^2 + (x + 3)^2 + (x - 4)^2 + (x - 8)^2
This simplifies to
5x^2 + 20x + 282 the minimum will at occur at the x value (-20) / (2 * 5) = -20 / 10 = -2
And the minimum value is
5(-2)^2 + 20(-2) + 282 =
20 - 40 + 282 =
262
