Complete the square in each parentheses by adding the
square of half the coefficient of X, Y and Z respectively
inside each parentheses on the left side of the equation,
and adding the same quantities to the right side.
Factor each parenthetical expression as a perfect square
and combine the terms on the right:
That's the equation of a sphere with center (5,-8,6) and
radius 0. So it is the equation of a sphere that is
degenerated into the point (5,-8,6) in 3D space.
X = 5, Y = -8, Z = 6, So X+Y+Z = 5-8+6 = 3
Edwin
