Completing the Square

In this section, we begin by refreshing our memory on quadratic equations. We review standard form, and how to solve a quadratic equation when it’s factorable. Next, we learn about the square root property. This property allows us to solve an equation where there is a perfect square on one side that is equal to a constant on the other. In many cases, we aren’t given this exact scenario. When this occurs, we can use a method known as completing the square. This allows us to solve any quadratic equation using the square root property. We will be algebraically manipulating the equation in such a way that the left side is a perfect square trinomial and the right side is a constant. The left side can then be factored into a binomial squared. Once this is done, we can use the square root property to obtain a solution.