College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises - Page 138: 20


$x=-5$ or $ x=-1$ or $ x=-9$

Work Step by Step

$(x+5)^4-16(x+5)^2=0$ Factor $(x+5)^2$ $\Rightarrow (x+5)^2\bigg((x+5)^2-16\bigg)=0$ Expand $\Rightarrow (x+5)^2\bigg((x^2+10x+25)-16\bigg)=0$ Collect $\Rightarrow (x+5)^2\bigg(x^2+10x+9\bigg)=0$ Factor $\Rightarrow (x+5)^2\bigg((x+1)(x+9)\bigg)=0$ $\Rightarrow (x+5)^2(x+1)(x+9)=0$ Zero-Product Property $ x+5=0$ or $ x+1=0$ or $ x+9=0$ Solve $x=-5$ or $ x=-1$ or $ x=-9$
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