Write the equation of the sphere in standard form. x^2 + y^2 + z^2 + 2x - 2y - 2z = 22

Given:

x^2 + y^2 + z^2 + 2x - 2y - 2z = 22

group the variables

x^2+2x + y^2-2y + z^2-2z = 22

then complete the squares

x^2+2x+1 + y^2-2y+1 + z^2-2z+1 = 22 + 1 + 1 + 1

factor and simplify

(x+1) ^2 + (y-1) ^2 + (z-1) ^2 = 5^2

Interpretation:

The centre of the sphere is at (-1,1,1) with a radius of 5