College Algebra 7th Edition

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

Chapter P, Prerequisites - Section P.8 - Solving Basic Equations - P.8 Exercises: 71

Answer

Thus, the solutions to the given equation are $-5$ and $1$.

Work Step by Step

Add 81 to both sides of the equation to obtain: $(x+2)^4=81$ Write $81$ as $3^4$ to obtain: $(x+2)^4=3^4$ Take the fourth root of both sides: $x+2 = \pm \sqrt[4]{3^4} \\x+2 = \pm3$ Subtract $2$ to both sides of the equation: $x=\pm3 - 2 \\x=-2 \pm 3$ The solutions are: $x_1=-2+3 = 1 \\x_2=-2-3=-5$ Thus, the solutions to the given equation are $-5$ and $1$.
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