Previously in this video series, students saw that a squared expression of the form (x + n)² is equivalent to x² + 2nx + n². This means that, when written in standard form ax² + bx + c (where a is 1), b is equal to 2n and c is equal to n². Here, students begin to reason the other way around. They recognize that if ax² + bx + c is a perfect square, then the value being squared to get c is half of b, or (b/2)². Students use this insight to build perfect squares, which they then use to solve quadratic equations.

Students learn that if we rearrange and rewrite the expression on one side of a quadratic equation to be a perfect square, that is, if we complete the square, we can find the solutions of the equation.

Rearranging parts of an equation strategically so that it can be solved requires students to make use of structure (MP7). Maintaining the equality of an equation while transforming it prompts students to attend to precision (MP6).

Algebra 1, Episode 20: Unit 7, Lesson 12 | Illustrative Math