And square root the equation, this will give the same thing. No matter on which side 1 is, it's the same, you choose what you do by intuition.
Now, a slight difference. Your teachers' method can apply to any case, that is to say if you have for example , your teachers' method will better fit in it.
Or another *slight* difference, is if you're asked to factorize x²-4x+3, you'll use your teachers' steps.