Completing the Square Versus The Quadratic Formula

My college algebra class is learning to find the zeros of polynomial functions, so we are solving lots of quadratic equations.  If the quadratic expression is not easily factorable, I have been saying. “Just use the Quadratic Formula.”  Here is an example.

Quadratic Formula with Even Linear Coefficient

Note all of the awkward simplifying at the end.  It dawned on me that if the coefficient of the x term is even, completing the square is much easier as can be seen here.

Completing the Square with Even Linear Coefficient

The quadratic formula is simply completing the square as a compact expression, but when the coefficient of the x term is even, completing the square just seems cleaner.  Not so with odd coefficients as can be seen here.

Completing the Square with Odd Linear Coefficient

Versus:

Quadratic Formula with Odd Linear Coefficient

So, at least in my classroom demonstrations:  Even linear coefficients – complete the square; Odd linear coefficients – quadratic formula.