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: 35

Answer

$y=-\dfrac{1}{4}\pm\dfrac{\sqrt{23}}{4}i$

Work Step by Step

$\dfrac{2}{5}y^{2}+\dfrac{1}{5}y+\dfrac{3}{5}=0$ Multiply the whole equation by $5$ to avoid working with fractions: $5\Big(\dfrac{2}{5}y^{2}+\dfrac{1}{5}y+\dfrac{3}{5}=0\Big)$ $2y^{2}+y+3=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=2$, $b=1$ and $c=3$. Substitute: $x=\dfrac{-1\pm\sqrt{1^{2}-4(2)(3)}}{2(2)}=\dfrac{-1\pm\sqrt{1-24}}{4}=...$ $...=\dfrac{-1\pm\sqrt{-23}}{4}=\dfrac{-1\pm\sqrt{23}i}{4}=-\dfrac{1}{4}\pm\dfrac{\sqrt{23}}{4}i$
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