![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, Andrea Honeycutt Mathis Use the information below to generate a citation. Then you must include on every digital page view the following attribution: Rule for Using the Quadratic Formula The equation. x equals the opposite of b, plus or minus the square root of b squared minus 4 a c, all divided by 2 a. ![]() You can read this formula as: Where a 0 and b 2 4 a c 0. If you are redistributing all or part of this book in a digital format, Quadratic formula is used to solve any kind of quadratic equation. Mathematicians look for patterns when they. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this’ The answer is ‘yes’. Sometimes, we will need to do some algebra to get the equation into standard form before we can use the Quadratic Formula. Remember, to use the Quadratic Formula, the equation must be written in standard form, ax2 + bx + c 0. When we solved quadratic equations in the last section by completing the square, we took the same steps every time. Solve by using the Quadratic Formula: 5b2 + 2b + 4 0 5 b 2 + 2 b + 4 0. Then you must include on every physical page the following attribution: Solve Quadratic Equations Using the Quadratic Formula. 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 Then, we do all the math to simplify the expression. To use the Quadratic Formula, we substitute the values of a, b, and c into the expression on the right side of the formula. 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. The solutions to a quadratic equation of the form ax2 + bx + c 0, a 0 are given by the formula: x b ± b2 4ac 2a. We start with the standard form of a quadratic equation and solve it for x by completing the square. Now we will go through the steps of completing the square using the general form of a quadratic equation to solve a quadratic equation for x. We have already seen how to solve a formula for a specific variable ‘in general’, so that we would do the algebraic steps only once, and then use the new formula to find the value of the specific variable. In this section we will derive and use a formula to find the solution of a quadratic equation. Mathematicians look for patterns when they do things over and over in order to make their work easier. See examples of using the formula to solve a variety of equations. Then, we plug these coefficients in the formula: (-b (b-4ac))/ (2a). First, we bring the equation to the form ax+bx+c0, where a, b, and c are coefficients. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this?’ The answer is ‘yes’. The quadratic formula helps us solve any quadratic equation. Solving quadratic equations is no modern accomplishment. When we solved quadratic equations in the last section by completing the square, we took the same steps every time. History of the Quadratic Formula Early History. Solve Quadratic Equations Using the Quadratic Formula ![]() If you missed this problem, review Example 8.76. ![]()
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