Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.4 Equations - R.4 Exercises - Page R-16: 25


$\displaystyle \frac{-1+\sqrt{73}}{6}\approx 1.257$ $\displaystyle \frac{-1-\sqrt{73}}{6}\approx-1.591$

Work Step by Step

Set the $RHS$ to 0 by subtracting 6 from both sides $3k^{2}+k=6\qquad.../-6$ $3k^{2}+k-6=0$ Use the quadratic formula: (For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ ) $k=\displaystyle \frac{-1\pm\sqrt{1-4(3)(-6)}}{2(3)}=\frac{-1\pm\sqrt{1+72}}{6}$ $k=\displaystyle \frac{-1\pm\sqrt{73}}{6}$ Solutions: $\displaystyle \frac{-1+\sqrt{73}}{6}\approx 1.257$ and $\displaystyle \frac{-1-\sqrt{73}}{6}\approx-1.591$.
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