Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Review: 61


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

Work Step by Step

Given $x^2+x+7=0$ $a=1,\ b=1,\ c=7$ Using the quadratic formula: $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} , $ we have: $\dfrac{-1\pm \sqrt{1^2-4\times 1\times 7}}{2\times 1} = \dfrac{-1\pm \sqrt{-27}}{2} = \dfrac{-1\pm \sqrt{27}i}{2} = \dfrac{-1\pm 3\sqrt{3}i}{2}$ Therefore the solutions are: $x_{1}= \dfrac{-1 + 3\sqrt{3}i}{2}$ and $x_{2}= \dfrac{-1\ - 3\sqrt{3}i}{2}$
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