Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 8 - Sections 8.1-8.3 - Integrated Review - Summary on Solving Quadratic Equations: 20

Answer

$x=\dfrac{-5\pm\sqrt{17}}{4}$

Work Step by Step

Using the properties of equality, the given quadratic equation, $ 2x^2=-5x-1 ,$ is equivalent to \begin{array}{l}\require{cancel} 2x^2+5x+1=0 .\end{array} Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the quadratic equation above are \begin{array}{l}\require{cancel} x=\dfrac{-5\pm\sqrt{(5)^2-4(2)(1)}}{2(2)} \\\\ x=\dfrac{-5\pm\sqrt{25-8}}{4} \\\\ x=\dfrac{-5\pm\sqrt{17}}{4} .\end{array}
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