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: 46


$x=${$\dfrac{5 - \sqrt {73}}{2},\dfrac{5 + \sqrt {73}}{2}$}

Work Step by Step

Given: $\dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{1}{4}$ Re-write the given equation as: $x^2-5x-12=0$ 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 $x=\dfrac{-(-5) \pm \sqrt{(-5)^2-4(1)(-12)}}{2(1)}$ or, $x=\dfrac{5 \pm \sqrt {73}}{2}$ Hence, our solution set is: $x=${$\dfrac{5 - \sqrt {73}}{2},\dfrac{5 + \sqrt {73}}{2}$}
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