In this lesson, students solve solving quadratic equations whose solutions are non-real complex numbers. Students complete the square to analyze the conditions that lead quadratic equations with real coefficients to have 1 real solution, 2 real solutions, or 2 non-real solutions.

One activity is optional because it goes beyond the depth of understanding required by the standards.

Students are making use of structure when they complete the square with to understand the relationship between the constant coefficient, the coefficient of , the number of solutions, and the type of solutions (MP7).