Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises: 75

Answer

$n = 5.236, 0.764$

Work Step by Step

$4(n-3)^{2} + 10 = 30$ $4[n(n-3)-3(n-3)] = 30 - 10$ $4[n^{2} - 3n - 3n + 9] = 20$ $4[n^{2} - 6n + 9] = 20$ $4n^{2} - 24n + 36 = 20$ $4n^{2} - 24n + 36 - 20 = 0$ $4n^{2} - 24n + 16 = 0$ $4(n^{2} - 6n + 4) = 0$ $n = \frac{-(-6)±\sqrt {(-6)^{2}-4(1)(4)}}{2(1)}$ $n = \frac{6±\sqrt {36-4(1)(4)}}{2}$ $n = \frac{6±\sqrt {36-16}}{2}$ $n = \frac{6±\sqrt {20}}{2}$ $n = \frac{6±2\sqrt {5}}{2}$ $n = \frac{3±\sqrt {5}}{1}$ $n = 3±\sqrt {5}$ $n = 5.236, 0.764$
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