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: 90


The solution set in standard form is $$\Big\{-\frac{3}{4}\pm\frac{\sqrt7}{4}i\Big\}$$

Work Step by Step

$$2x^2+3x=-2$$ First, write the equation in standard form. $$2x^2+3x+2=0$$ Now use the quadratic formula. $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ As $a=2, b=3, c=2$ $$x=\frac{-3\pm\sqrt{3^2-4\times2\times2}}{2\times2}$$ $$x=\frac{-3\pm\sqrt{9-16}}{4}$$ $$x=\frac{-3\pm\sqrt{-7}}{4}$$ Now we rewrite $\sqrt{-7}=i\sqrt7$ $$x=\frac{-3\pm i\sqrt7}{4}$$ The solution set in standard form is $$\Big\{-\frac{3}{4}\pm\frac{\sqrt7}{4}i\Big\}$$
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