lets begin

Question

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.