In this lesson, students begin to reason that if is a perfect square, then the value being squared to get is half of , or . Students use this insight to build perfect squares, which they then use to solve quadratic equations.

Students learn that rearranging and rewriting the expression on one side of a quadratic equation to be a perfect square, or completing the square, can help 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).