Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Quiz for Lessons 4.5-4.7 - Page 291: 6


$x=\displaystyle \pm i\frac{\sqrt{14}}{7}$

Work Step by Step

$ 7x^{2}-4=-6\qquad$ ...add $4$ to each side of the expression. $ 7x^{2}=-2\qquad$ ...divide each term with $7$. $ x^{2}=-\displaystyle \frac{2}{7}\qquad$ ...take square roots of each side. $ x=\pm\sqrt{-\frac{2}{7}}\qquad$ ...write in terms of $i$. $ x=\displaystyle \pm i\frac{\sqrt{2}}{\sqrt{7}}\qquad$ ...rationalize the radical by multiplying both the numerator and denominator with $\sqrt{7}$. $\displaystyle \frac{\sqrt{2}}{\sqrt{7}}=\frac{\sqrt{2}\cdot\sqrt{7}}{\sqrt{7}\cdot\sqrt{7}}=\frac{\sqrt{14}}{7}$ $x=\displaystyle \pm i\frac{\sqrt{14}}{7}$
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