In this lesson, students complete the square to solve quadratic equations in which the squared term has a coefficient other than 1.

Students begin by noticing that the structure for expanding expressions such as can also be used to expand expressions such as . The expanded expression is always . If the perfect square in standard form is , then and . Recognizing this structure allows students to complete the square for expressions of the form when is not 1, and then to solve equations with such expressions (MP7).

Completing the square when is not 1 can be rather laborious, even when is a perfect square and is an even number. It is even more time consuming and complicated when is not a perfect square and is not an even number. Students are not expected to master the skill of solving quadratic equations with by completing the square. In fact, they should see that this method has its limits and seek a more efficient strategy.

This lesson aims only to show that this type of quadratic equation can be solved by completing the square and exposing students to how it can be done. This exposure provides some background knowledge that will be helpful when students derive the quadratic formula later.