Objective: Solve quadratic equations by completing the square.
Completing the square is a process in which a constant is added to a binomial in order to create a perfect square trinomial. For example, to complete the square on the binomial x2 + 6x, the constant which must be added is 9, since x2 + 6x + 9 is a perfect square trinomial. This process is useful in solving quadratic equations because once the equation contains a perfect square trinomial, the principle of square roots can be applied to find the solutions. The video below contains an introduction to the process of completing the square.
In order to solve a quadratic equation by completing the square, it is helpful to first write one side of the equation in the form x2 + bx. After this is done, it is easy to complete the square by adding the square of one-half of b to both sides of the equation, and then solve the equation using the principle of square roots. Watch the video below to see several examples of how to solve quadratic equations by completing the square.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.