College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.2 - Quadratic Equations - 1.2 Assess Your Understanding: 59

Answer

$\displaystyle x=\frac{3\pm\sqrt{29}}{10}$

Work Step by Step

$\displaystyle \frac{5}{3}x^{2}-x=\frac{1}{3}$ We multiply by $3$: $3(\displaystyle \frac{5}{3}x^{2}-x)=3*\frac{1}{3}$ $5x^{2}-3x=1$ $5x^{2}-3x-1=0$ We solve using the quadratic formula ($a=5,\ b=-3,\ c=-1$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $\displaystyle x=\frac{-(-3)\pm\sqrt{(-3)^{2}-4*5*-1}}{2*5}$ $\displaystyle x=\frac{3\pm\sqrt{9+20}}{10}$ $\displaystyle x=\frac{3\pm\sqrt{29}}{10}$
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