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. This last equation is the Quadratic Formula. X = − b ± b 2 − 4 a c 2 a x = − b ± b 2 − 4 a c 2 a X = − b 2 a ± b 2 − 4 a c 2 a x = − b 2 a ± b 2 − 4 a c 2 a X + b 2 a = ± b 2 − 4 a c 2 a x + b 2 a = ± b 2 − 4 a c 2 aĪdd − b 2 a − b 2 a to both sides of the equation. X + b 2 a = ± b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 ( x + b 2 a ) 2 = − c a + b 2 4 a 2 ( x + b 2 a ) 2 = − c a + b 2 4 a 2įind the common denominator of the right side and writeĮquivalent fractions with the common denominator. The left side is a perfect square, factor it. X 2 + b a x + b 2 4 a 2 = − c a + b 2 4 a 2 x 2 + b a x + b 2 4 a 2 = − c a + b 2 4 a 2 Learn how to use the quadratic formula, the discriminant, and related concepts with examples and FAQs. Enter your own equation or use the calculator to find the solutions, roots, and factors of a quadratic equation. ( 1 2 b a ) 2 = b 2 4 a 2 ( 1 2 b a ) 2 = b 2 4 a 2 Solve any quadratic equation using the quadratic formula or the discriminant. Make leading coefficient 1, by dividing by a.Ī x 2 a + b a x = − c a a x 2 a + b a x = − c a We start with the standard form of a quadratic equationĪnd solve it for x by completing the square.Ī x 2 + b x + c = 0 a ≠ 0 a x 2 + b x + c = 0 a ≠ 0
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