College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.6 - Other Types of Equations and Applications - Summary Exercises on Solving Equations - Page 136: 19

Answer

$x=3$ or $x=11$

Work Step by Step

We are given: $(14-2x)^{2/3}=4$ We raise both sides to the $3$rd power: $[(14-2x)^{2/3}]^{3}=4^{3}$ $(14-2x)^{2}=64$ $(14-2x)(14-2x)=64$ And distribute: $196-56x+4x^{2}=64$ $196-56x+4x^{2}-64=0$ $4x^{2}-56x+132=0$ And factor: $4(x^{2}-14x+33)=0$ $4(x-3)(x-11)=0$ Equate each factor to zero, then solve each equation for $x$: $4(x-3)=0$ or $(x-11)=0$ $(x-3)=0$ or $(x-11)=0$ $x=3$ or $x=11$
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