Distance between spheres help

Question

The equations x² + y² + z² - 6z = -8 and x² - 18x + y² + 14y + z² = -126 represent spheres in three dimensions. Find the distance between these two spheres. Include at least three decimal places in your answer.

Answer 1

x^2 +y^2 + z^2-6z+9 = -8+9

complete the squares

x^2 +y^2 +(z-3)^2 = 1 is a sphere with center (0,0,3) and radius = 1^(1/2)

x^2-18x+81 +y^2+14y+49 +z^2 =-126 +81+49

complete the squares

(x-9)^2 + (y+7)^2 +z^2 = 4 is a sphere with center (9,-7,0) and radius = 4^(1/2)

calculate the distance between the centers, then subtract [1+4^(1/2)] the sum of their radii

that leaves the distance between the closest points on the edge of each sphere

the difference between centers (9,-7,0) and (0,0,3) is

square root of (81+49+9) = sqr139

distance between the two spheres = sqr139 -1-4^(1/2)

use a calculator

= sqr136 -3

=11.6619-3

=8.6619