Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.6 - Complex Numbers - 1.6 Exercises: 72

Answer

$x=-\dfrac{1}{4}\pm\dfrac{\sqrt{15}}{4}i$

Work Step by Step

$x^{2}+\dfrac{1}{2}x+1=0$ Multiply the whole equation by $2$: $2\Big(x^{2}+\dfrac{1}{2}x+1=0\Big)$ $2x^{2}+x+2=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=2$, $b=1$ and $c=2$. Substitute the known values in the formula: $x=\dfrac{-1\pm\sqrt{1^{2}-4(2)(2)}}{2(2)}=\dfrac{-1\pm\sqrt{1-16}}{4}=...$ $...=\dfrac{-1\pm\sqrt{-15}}{4}=\dfrac{-1\pm\sqrt{15}i}{4}=-\dfrac{1}{4}\pm\dfrac{\sqrt{15}}{4}i$ The answer is $x=-\dfrac{1}{4}\pm\dfrac{\sqrt{15}}{4}i$
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