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