Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.2 The Quadratic Formula - 11.2 Exercise Set - Page 713: 41

Answer

$$x=5+\sqrt{53},\:x=5-\sqrt{53}$$

Work Step by Step

Solving by plugging in the given value and then using the quadratic formula, we find: $$ 1\cdot \:x\left(x+4\right)=\frac{7}{x}x\left(x+4\right)+\frac{7}{x+4}x\left(x+4\right)\\ x\left(x+4\right)=7\left(x+4\right)+7x\\ x^2-10x-28=0\\ x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-28\right)}}{2\cdot \:1}\\ x=5+\sqrt{53},\:x=5-\sqrt{53}$$
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