Let's begin with
x2 + bx
and notice that the x2 hold a coefficient of one. That is needed in order to do this. Now, to this lets add ( b /2) 2 . Doing this gives the given factorable quadratic equation.
x2 + bx + ( b /2)2 = (x+(b/2))2
This procedure is called accomplishing the square and if we do all the arithmetic properly we can guarantee that the quadratic will factor as a perfect square.
Let's do a couple of examples for completing the square before looking at how we employ this to solve out quadratic equations.