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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