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: 31

Answer

$y=-\dfrac{1}{2}\pm\dfrac{\sqrt{5}}{10}i$

Work Step by Step

$10y^{2}+10y+3=0$ Use the quadratic formula to solve this equation. The formula is $y=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=10$, $b=10$ and $c=3$ Substitute: $y=\dfrac{-10\pm\sqrt{10^{2}-4(10)(3)}}{2(10)}=\dfrac{-10\pm\sqrt{100-120}}{20}=...$ $...=\dfrac{-10\pm\sqrt{-20}}{20}=\dfrac{-10\pm\sqrt{20}i}{20}=\dfrac{-10\pm2\sqrt{5}i}{20}=...$ $...=-\dfrac{1}{2}\pm\dfrac{\sqrt{5}}{10}i$
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