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: 36

Answer

$x=-4\pm2i$

Work Step by Step

$\dfrac{1}{8}x^{2}+x+\dfrac{5}{2}=0$ Multiply the whole equation by $8$ to avoid working with fractions: $8\Big(\dfrac{1}{8}x^{2}+x+\dfrac{5}{2}=0\Big)$ $x^{2}+8x+20=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here $a=1$, $b=8$ and $c=20$. Substitute: $x=\dfrac{-8\pm\sqrt{8^{2}-4(1)(20)}}{2(1)}=\dfrac{-8\pm\sqrt{64-80}}{2}=...$ $...=\dfrac{-8\pm\sqrt{-16}}{2}=\dfrac{-8\pm4i}{2}=-4\pm2i$
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