In this video lesson, students learn that completing the square can be used to solve any quadratic equation, including equations that involve rational numbers that are not integers. Students notice that the process of completing the square is the same when the equations involve messier numbers as when they have simple integers, but the calculations may be more time consuming and prone to error. An error-analysis activity highlights some common errors related to completing the square.

Completing the square for quadratic expressions that are more elaborate encourages students to look for and make use of the same structure that helped them when they were working with less complicated expressions (MP7).

Algebra 1, Episode 21: Unit 7, Lesson 13 | Illustrative Math