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: 26

Answer

$x=\dfrac{-3\pm\sqrt{19}}{5}$

Work Step by Step

Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the given quadratic equation, $ 5x^2+6x-2=0 ,$ are \begin{array}{l}\require{cancel} x=\dfrac{-6\pm\sqrt{6^2-4(5)(-2)}}{2(5)} \\\\ x=\dfrac{-6\pm\sqrt{36+40}}{10} \\\\ x=\dfrac{-6\pm\sqrt{76}}{10} \\\\ x=\dfrac{-6\pm\sqrt{4\cdot19}}{10} \\\\ x=\dfrac{-6\pm\sqrt{(2)^2\cdot19}}{10} \\\\ x=\dfrac{-6\pm2\sqrt{19}}{10} \\\\ x=\dfrac{2(-3\pm\sqrt{19})}{10} \\\\ x=\dfrac{\cancel{2}(-3\pm\sqrt{19})}{\cancel{2}(5)} \\\\ x=\dfrac{-3\pm\sqrt{19}}{5} .\end{array}
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