(x-a)^2 + (y-b)^2 + (z-c)^2 = d is a sphere centered at a, b, c with radius square root of d.
Now regarding the first post, I can bring the z over to the left hand side:
x^2 + y^2 + z^2 - z = 0
Then complete the square
x^2 + y^2 + (z - 1/2)^2 -1/4 = 0
[(z - 1/2)^2 = z^2 - 2*1/2 z...