Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.1 Complex Numbers - 8.1 Exercises - Page 364: 89


The solution set in standard form is $$\Big\{-\frac{2}{3}\pm\frac{\sqrt2}{3}i\Big\}$$

Work Step by Step

$$3x^2+2=-4x$$ First, write the equation in standard form. $$3x^2+4x+2=0$$ Now use the quadratic formula. $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ As $a=3, b=4, c=2$ $$x=\frac{-4\pm\sqrt{4^2-4\times3\times2}}{2\times3}$$ $$x=\frac{-4\pm\sqrt{16-24}}{6}$$ $$x=\frac{-4\pm\sqrt{-8}}{6}$$ Now we rewrite $\sqrt{-8}=i\sqrt8=2i\sqrt2$ $$x=\frac{-4\pm2i\sqrt2}{6}$$ Finally, we simplify $$x=\frac{-2\pm i\sqrt2}{3}$$ The solution set in standard form is $$\Big\{-\frac{2}{3}\pm\frac{\sqrt2}{3}i\Big\}$$
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