![]() ![]() You can find the values for which this quadratic equation equals 0, so the equation has one or two answers. Solve the portion in parentheses with the quadratic formula if you can’t factor it manually. This article has been viewed 1,094,612 times. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. The quadratic equation in its standard form is ax 2 + bx + c 0, where a and b are the coefficients, x is the variable, and c is the constant term. There are 10 references cited in this article, which can be found at the bottom of the page. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. ![]() After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. This article was co-authored by David Jia and by wikiHow staff writer, Christopher M. 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. A quadratic equation is an equation of the form ax 2 + bx + c 0, where a 0 a 0.Quadratic equations differ from linear equations by including a quadratic term with the variable raised to the second power of the form ax 2. We guarantee that this term will be present in the equation by requiring a 0 a 0. The only requirement here is that we have an x2 x 2 in the equation. First, the standard form of a quadratic equation is. Then you must include on every digital page view the following attribution: So, we are now going to solve quadratic equations. 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 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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