Algebra: A Combined Approach (4th Edition)

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

Chapter 12 - Cumulative Review: 41

Answer

$x_{1}=\dfrac{2 + \sqrt{10}}{2}$ and $x_{2}=\dfrac{2- \sqrt{10}}{2}$

Work Step by Step

Given $2x^2-4x=3 \longrightarrow 2x^2-4x-3=0$ $a = 2, \ b = -4, \ c = -3$ Using the quadratic formula $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a} , $ we have: $\dfrac{-(-4)\pm \sqrt{(-4)^2-4\times 2\times (-3)}}{2\times2} = \dfrac{4\pm \sqrt{16+24}}{4} = \dfrac{4\pm \sqrt{40}}{4} = \dfrac{4\pm 2\sqrt{10}}{4} = \dfrac{2\pm \sqrt{10}}{2}$ Therefore, the solutions are $x_{1}=\dfrac{2 + \sqrt{10}}{2}$ and $x_{2}=\dfrac{2- \sqrt{10}}{2}$
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