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 guides viewers through three distinct examples that increase in complexity, beginning with a standard equation with a leading coefficient of one, moving to an equation involving odd coefficients resulting in fractions, and concluding with a challenging problem where the leading coefficient is greater than one. Each step is clearly explained visually and verbally, demonstrating the logic behind algebraic manipulations. The video explores key mathematical themes including isolating variables, the properties of equality, factoring perfect square trinomials, and arithmetic operations with fractions. It explicitly addresses how to handle the leading coefficient by factoring it out and ensuring that the equation remains balanced when adding terms to both sides. The tutorial also emphasizes the importance of verifying solutions by substituting them back into the original equation. For educators, this video is an excellent resource for Algebra I and Algebra II classrooms. It breaks down a procedural concept that students often find difficult into manageable steps. Teachers can use this video to introduce the topic, as a remediation tool for students struggling with the algorithm, or as a flipped classroom assignment. The progression from simple integers to complex fractions allows for differentiated instruction, catering to various skill levels within the same class.