If a quadratic equation can be factored, it is written as a product of linear terms. Factoring means finding expressions that can be multiplied together to give the expression on one side of the equation. Often the easiest method of solving a quadratic equation is factoring. They are used in countless ways in the fields of engineering, architecture, finance, biological science, and, of course, mathematics. For example, equations such as 2 x 2 + 3 x − 1 = 0 2 x 2 + 3 x − 1 = 0 and x 2 − 4 = 0 x 2 − 4 = 0 are quadratic equations. Solving Quadratic Equations by FactoringĪn equation containing a second-degree polynomial is called a quadratic equation. If there is a limited amount of space and we desire the largest monitor possible, how do we decide which one to choose? In this section, we will learn how to solve problems such as this using four different methods. Proportionally, the monitors appear very similar. The computer monitor on the left in Figure 1 is a 23.6-inch model and the one on the right is a 27-inch model. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. Together you can come up with a plan to get you the help you need. See your instructor as soon as you can to discuss your situation. You should get help right away or you will quickly be overwhelmed. …no-I don’t get it! This is a warning sign and you must not ignore it. Is there a place on campus where math tutors are available? Can your study skills be improved? Whom can you ask for help? Your fellow classmates and instructor are good resources. It is important to make sure you have a strong foundation before you move on.
In math, every topic builds upon previous work. …with some help: This must be addressed quickly because topics you do not master become potholes in your road to success. What did you do to become confident of your ability to do these things? Be specific.
Reflect on the study skills you used so that you can continue to use them. …confidently: Congratulations! You have achieved the objectives in this section. Ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. We defined the square root of a number in this way:Įxplain why the equation y 2 + 8 = 12 y 2 + 8 = 12 has two solutions. These equations are all of the form x 2 = k x 2 = k. But what happens when we have an equation like x 2 = 7 x 2 = 7? Since 7 is not a perfect square, we cannot solve the equation by factoring. We can easily use factoring to find the solutions of similar equations, like x 2 = 16 x 2 = 16 and x 2 = 25 x 2 = 25, because 16 and 25 are perfect squares. x = ± 3 (The solution is read ‘ x is equal to positive or negative 3.’) x = 3, x = −3 Combine the two solutions into ± form. ( x − 3 ) = 0, ( x + 3 ) = 0 Solve each equation. ( x − 3 ) ( x + 3 ) = 0 Use the Zero Product Property. x = ± 3 (The solution is read ‘ x is equal to positive or negative 3.’) x 2 = 9 Put the equation in standard form. X 2 = 9 Put the equation in standard form.
