Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.3 - Integrated Review - Summary on Solving Quadratic Equations: 26

Answer

$x_{1}= \dfrac{-3 + \sqrt{19}}{5} $ and $x_{2} = \dfrac{-3 - \sqrt{19}}{5} $

Work Step by Step

Given $5x^2+6x-2=0$ $a= 5, \ b=6, \ c=-2$ Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ we have: $\dfrac{-6 \pm \sqrt{6^2-4 \times 5\times (-2)}}{2 \times 5} = \dfrac{-6 \pm \sqrt{36+40}}{10} = \dfrac{-6 \pm \sqrt{76}}{10} = \dfrac{-6 \pm 2\sqrt{19}}{10} = \dfrac{-3 \pm \sqrt{19}}{5} $ Therefore the solutions are $x_{1}= \dfrac{-3 + \sqrt{19}}{5} $ and $x_{2} = \dfrac{-3 - \sqrt{19}}{5} $
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