College Algebra (11th Edition)

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

Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises - Page 112: 32


$x=\left\{ \dfrac{-1-2\sqrt{5}}{4},\dfrac{-1+2\sqrt{5}}{4} \right\} $

Work Step by Step

Taking the square root of both sides, the solutions to the given equation, $ (4x+1)^2=20 ,$ are \begin{array}{l}\require{cancel} 4x+1=\pm\sqrt{20} \\\\ 4x+1=\pm\sqrt{4\cdot5} \\\\ 4x+1=\pm\sqrt{(2)^2\cdot5} \\\\ 4x+1=\pm2\sqrt{5} \\\\ 4x=-1\pm2\sqrt{5} \\\\ x=\dfrac{-1\pm2\sqrt{5}}{4} .\end{array} Hence, the solutions are $ x=\left\{ \dfrac{-1-2\sqrt{5}}{4},\dfrac{-1+2\sqrt{5}}{4} \right\} .$
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