Elementary Technical Mathematics

Published by Brooks Cole
ISBN 10: 1285199197
ISBN 13: 978-1-28519-919-1

Chapter 16 - Cumulative Review - Page 568: 12


The solution of the equation $7{{x}^{2}}+2x+15=0$ is $x=-0.143\pm 1.46i$.

Work Step by Step

Use the quadratic formula $x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$, $\begin{align} & x=\frac{-2\pm \sqrt{{{2}^{2}}-4\left( 7 \right)\left( 15 \right)}}{2\left( 7 \right)} \\ & =\frac{-2\pm \sqrt{4-420}}{14} \\ & =\frac{-2\pm \sqrt{-416}}{14} \end{align}$ $\sqrt{-1}=i$ and here $i$ is the imaginary number, $\begin{align} & x=\frac{-2\pm \sqrt{-416}}{14} \\ & =\frac{-2\pm \sqrt{416}i}{14} \\ & =\frac{-2}{14}\pm \frac{\sqrt{416}i}{14} \\ & =-0.143\pm 1.46i \end{align}$
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