Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Section 8.2 - The Quadratic Formula - Exercise Set - Page 608: 42

Answer

$x=${$\dfrac{3 \pm \sqrt{11}}{2}$}

Work Step by Step

Given: $\dfrac{x^2}{3}-x-\dfrac{1}{6}=0$ Re-write the equation as: $2x^2-6x-1=0$ Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ This implies that $x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(2)(-1)}}{2(2)}$ or, $x=\dfrac{6 \pm \sqrt{44}}{4}$ or, $x=\dfrac{6 \pm 2\sqrt{11}}{4}$ Hence, our solution is: $x=${$\dfrac{3 \pm \sqrt{11}}{2}$}
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