How to Solve Quadratic Equations by Completing the Square

The Organic Chemistry Tutor

This instructional video provides a comprehensive tutorial on solving quadratic equations using the method of completing the square. The narrator systematically guides viewers through five distinct examples, starting with simple equations where the leading coefficient is one and moving to more complex problems involving negative leading coefficients, coefficients greater than one, and calculations requiring fraction arithmetic. The video utilizes a clear, step-by-step whiteboard style to demonstrate the algebraic manipulations required to isolate variables and solve for x. The content focuses on the procedural fluency of algebra, highlighting key techniques such as moving the constant term, halving the middle coefficient to determine the value to add to both sides, and factoring perfect square trinomials. It also covers how to handle irrational roots (leaving answers in radical form vs. decimal approximations) and how to manage fractions when the leading coefficient does not divide evenly into the other terms. The narrator offers practical tips for mental math and factoring shortcuts that streamline the process. For educators, this video serves as an excellent resource for Algebra I and II classrooms. It can be used to introduce the concept of completing the square, reinforce procedural skills for struggling students, or serve as a review before introducing the Quadratic Formula. The varied complexity of the examples makes it suitable for differentiated instruction, allowing teachers to assign specific segments based on student proficiency levels.