how do i find the center of this sphere?

x^2+y^2+z^2+9x-9y+3z=19

first combine terms

(x^2 + 9x) + (y^2 - 9y) + (z^2 + 3z) = 19

complete the square for x,y and z which is (b/2a)^2 to get b^2 +-2ab +- b^2 = (a +- b)^2

x: 9/2, 81/4

y:9/2, 81/4

z:3/2, 9/4

Now we have the constants to complete the squares so we add them to x,y and z terms and also the other side of the equaton and we get

(x^2 + 9x + 81/4) + (y^2 - 9y - 81/4) + (z^2 + 3z + 9/4) = 19 + 81/4 - 81/4 + 9/4

Now factor and we get

(x + 9/2)^2 + (y - 9/2)^2 + (z - 3/2)^2 = 20 1/4 = 81/4

center is at (- 9/2,9/2,3/2)

Radius is sqrt(81/4) = 9/2

x^2 + 9x + (9/2)^2 + y^2 - 9y + (-9/2)^2 + z^2 + 3z + (3/2)^2 = 19 + (9/2)^2 + (-9/2)^2 + (3/2)^2

(x + 9/2)^2 + (y - 9/2)^2 + (z + 3/2)^2 = 19 + 81/4 + 81/4 + 9/4

The center is at: (-9/2 , 9/2 , -3/2)