Determining the equation of a 3d sphere

[shemer77]

Homework Statement

The question is describe the surface whose equation is given
2x^2 +2y^2 + 2z^2 - 2x -3y +5z -2 = 0
now I know it needs to be grouped like this
(2x^2-2x) + (2y^2-3y) + (2z^2+5z)=2,
however from here I feel like I am forgetting some kind of basic algebra or something on how to factor this. Kind of stupid I know :/ Can someone please point me in the right direction?

 

[LCKurtz]

Complete the squares on all three variables.

 

[shemer77]

thats what I thought but how would it work in this situation, especially since you have the coefficients out on the first term?

 

[LCKurtz]

If you have something like 3x²+5x - 1, it is best to factor out the leading coefficient before completing the square:

$$3x^2 +5x -1 = 3(x^2+\frac 5 3 x - \frac 1 3)$$

and complete the square inside the parentheses:

$$3\left((x^2 +\frac 5 3 x + \frac {35}{36} + (-\frac 1 3 - \frac {35}{36})\right)<br /> =3\left((x+\frac 5 6)^2-\frac{47}{36}\right)$$