3 ways to solve a quadratic equation4/16/2024 ![]() ![]() 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 Here we make an attempt to multiply either the x variable term or the y variable term with a constant value such that either the x variable terms or the y variable terms cancel out and gives us the value of the other variable. ( x + b 2 a ) 2 = b 2 4 a 2 − 4 a c 4 a 2 ( x + b 2 a ) 2 = b 2 4 a 2 − 4 a c 4 a 2 The elimination method is another way to solve a system of linear equations. ( 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 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 Regardless of how you feel going into learning quadratic equations, know that you can conquer this, too. Now, we are opening a new tool: quadratics Quadratic equations may feel different, scary, exciting, or all of the above. You are able to create and interpret graphs of equations. 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 You conquered solving equations for the value of x. ![]()
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