How do you complete the square?

Completing the square is taking an equation in the form a₁x²+b₁x+c₁ and butting it into the form a₂(x+b₂)²+c₂Let's try an example:x²+4x+5First step is to make sure the coefficient of x² 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.= x²+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= x²+4x+4, but we want x²+4x+5. To make this we add 1 as our constant.Final answer: x²+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 x² 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.)