Completing the Square

In a perfect square trinomial, there is a relationship between the coefficient of the x-term and the constant term — the constant term is equal to the square of half the coefficient of the x-term. x^2+bx+(b/2)^2 This relationship can be used to form a perfect square trinomial by adding a constant c to any expression in the form x^2+bx. x^2+bx ⇒ x^2+bx+c The process of finding the constant c can be visualized by using algebraic tiles. Consider the following expression. x^2+6x The expression is represented using algebraic tiles. Then, a square is created by rearranging the existing tiles and adding more tiles. The following applet summarizes this process.

This process is called completing the square. To complete the square for an expression algebraically, these steps can be followed.