Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set: 32

Answer

$y=-1\pm\dfrac{\sqrt{6}}{3}i$

Work Step by Step

$3y^{2}+6y+5=0$ Use the quadratic formula to solve this equation. The formula is $y=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=3$, $b=6$ and $c=5$. Substitute: $y=\dfrac{-6\pm\sqrt{6^{2}-4(3)(5)}}{2(3)}=\dfrac{-6\pm\sqrt{36-60}}{6}=...$ $...=\dfrac{-6\pm\sqrt{-24}}{6}=\dfrac{-6\pm\sqrt{24}i}{6}=\dfrac{-6\pm2\sqrt{6}i}{6}=...$ $...=-1\pm\dfrac{\sqrt{6}}{3}i$
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