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: 14

Answer

$x=-3\pm\sqrt{7}$

Work Step by Step

$\dfrac{1}{6}x^{2}+x+\dfrac{1}{3}=0$ Multiply the whole equation by $6$ to avoid working with fractions: $6\Big(\dfrac{1}{6}x^{2}+x+\dfrac{1}{3}=0\Big)$ $x^{2}+6x+2=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=6$ and $c=2$ Substitute: $x=\dfrac{-6\pm\sqrt{6^{2}-4(1)(2)}}{2(1)}=\dfrac{-6\pm\sqrt{36-8}}{2}=\dfrac{-6\pm\sqrt{28}}{2}=...$ $...=\dfrac{-6\pm2\sqrt{7}}{2}=-3\pm\sqrt{7}$
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