Completing the square is taking an equation in the form a_{1}x^{2}+b_{1}x+c_{1} and butting it into the form a_{2}(x+b_{2})^{2}+c_{2}Let's try an example:x^{2}+4x+5First step is to make sure the coefficient of x^{2} is 1. In this case it's already done.Secondly we half the coefficient of x, and put that number into our brackets:(x+2)^{2}+const.= x^{2}+4x+5Now if we expand the left hand side of the equation, we can work out what constant to put at the end(x+2)^{2}= x^{2}+4x+4, but we want x^{2}+4x+5. To make this we add 1 as our constant.Final answer: x^{2}+4x+5=(x+2)^{2}+1(I would then go on to have them work through a couple of examples to check their basic understanding, before moving onto examples where coefficient of x^{2} is larger than 1, and where coefficient of x is odd or negative. In each case I would allow them to work it through themselves as much as possible and only prompt where necessary, since practice is the best way to solidify an idea.)