I certainly wouldn't choose only the method of taking ±square roots of both sides
because that method is only good for quadratic equations with no "x"-term.

I certainly wouldn't choose only to learn the factoring method because most
quadratic trinomials are not factorable over the rational numbers, so I
couldn't use it for most quadratic equations.

I wouldn't choose only to learn the method of completing the square, even
though all quadratic equations can be solved by using it, because the quadratic
formula is easier.

So I would choose to learn the quadratic formula because it is the easiest way to
have a method that can be used to solve ALL quadratic equations.

Edwin