4/21 Algebra Zoom class

The instructor introduces the final day of practice for the class, focusing on completing the square, applicable to fourth, fifth, and sixth periods. Students are informed about video notes and homework involving three videos, guide completion, and extra guided notes on the quadratic formula. The instructor also mentions leaving the answer key on the worksheet for students to check their work, emphasizing the importance of understanding the process and steps, not just the final answers.

The instructor provides a step-by-step guide on how to complete the square, starting with moving variable terms to one side of the equation and constants to the other. The process involves creating a perfect square trinomial and simplifying square roots. The example given is a quadratic equation where the instructor demonstrates adding and subtracting terms to both sides to complete the square, simplifying the square root of 63 into 3 times the square root of 7, and solving for the variable n.

The instructor addresses student questions about the method of completing the square, specifically on simplifying square roots and dealing with equations where the first term coefficient is not one. The discussion includes the importance of simplifying radicals when possible and handling fractions that result from the process. The instructor also clarifies the process for equations with terms like '2 plus x' and how to adjust for them.

The instructor tackles a complex problem involving fractions and coefficients different from one. The process involves dividing all terms by the coefficient to simplify the equation, moving fractions to the other side, and dealing with the resulting complications. The instructor emphasizes the importance of maintaining a common denominator and the method of multiplying by a fraction to take half of a term, as seen in the example where 13/9 is multiplied by 1/2 to find half of the term.

The instructor continues the process of completing the square with a focus on handling fractions and irrational numbers. The example provided involves creating a common denominator, simplifying the equation, and taking the square root of non-perfect squares. The instructor simplifies the square root of 925 by factoring out the square root of 25, resulting in an irrational number that cannot be simplified further.

The instructor works through the final steps of solving a complex quadratic equation with fractions, emphasizing the importance of simplifying the radical and rationalizing the denominator. The process includes factoring down the equation into a binomial format, taking the square root of both sides, and simplifying the resulting expression. The instructor confirms the correctness of the solution and relates it to the answer key.

The instructor organizes the class into groups for further work on the problems, offering individual assistance as needed. There is a focus on problem numbers 13 and 15, which are identified as potentially difficult. The instructor moves between rooms to help students with their work, answering questions, and ensuring understanding of the concepts taught.

The instructor clarifies the steps for completing the square, particularly the process of rationalizing the denominator. Students are shown how to adjust terms and simplify equations, with an emphasis on the correct format for the final answer. The discussion includes the rationale behind changing the format of the answer to match the answer key.

The session concludes with the instructor offering final assistance to students who stayed beyond the scheduled time. The instructor agrees to solve an additional problem, number 15, as a reward for the students' dedication. There is a sense of camaraderie as the instructor thanks the students for their hard work and invites them to join the main room for the final review.