When would you use Completing the square over using the Quadratic formula (vice versa) to find x?
Completing the square is the more fundamental idea (indeed, you use completing the square to derive the quadratic formula!), so it's always useful to know that method. In situations in which I need to create more symmetry than is already there, I'll complete the square; this is especially useful if I need to know the shifting of the x-axis. However, if I'm just given a quadratic equation and told to find the roots, you can bet I'll use the quadratic formula.