Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Review: 17


$x_{1}=\dfrac{1 + \sqrt{35}i}{9}$ and $x_{2}=\dfrac{1- \sqrt{35}i}{9}$

Work Step by Step

Given $9a^2+4=2a \longrightarrow 9a^2-2a+4=0$ $a=9, \ b=-2, \ c=4$ Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a} , $ we have: $\dfrac{-(-2) \pm \sqrt{(-2)^2-4\times 9\times 4}}{2\times 9} = \dfrac{2 \pm \sqrt{4-144}}{18} = \dfrac{2 \pm \sqrt{-140}}{18} = \dfrac{2 \pm \sqrt{140}i}{18} = \dfrac{2 \pm 2\sqrt{35}i}{18} = \dfrac{1 \pm \sqrt{35}i}{9}$ Therefore, the solutions are $x_{1}=\dfrac{1 + \sqrt{35}i}{9}$ and $x_{2}=\dfrac{1- \sqrt{35}i}{9}$
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