Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Review - Page 829: 16


$x_{1}=\dfrac{5 + \sqrt{143}i}{12}$ and $x_{2}=\dfrac{5 - \sqrt{143}i}{12}$

Work Step by Step

Given $6x^2+7=5x \longrightarrow 6x^2-5x+7=0$ $a=6, \ b=-5, \ c=7$ Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a} , $ we have: $\dfrac{-(-5) \pm \sqrt{(-5)^2-4\times 6\times 7}}{2\times 6} = \dfrac{5 \pm \sqrt{25-168}}{12} = \dfrac{5 \pm \sqrt{-143}}{12} = \dfrac{5 \pm \sqrt{143}i}{12}$ Therefore, the solutions are: $x_{1}=\dfrac{5 + \sqrt{143}i}{12}$ and $x_{2}=\dfrac{5 - \sqrt{143}i}{12}$
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