Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.3 - Integrated Review - Summary on Solving Quadratic Equations: 4

Answer

$x=\left\{ \dfrac{-5-2\sqrt{3}}{2},\dfrac{-5+2\sqrt{3}}{2} \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ (2x+5)^2=12 ,$ take the square root of both sides and simplify the resulting radical. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Taking the square root of both sides (Square Root Property), the equation above is equivalent to \begin{array}{l}\require{cancel} 2x+5=\pm\sqrt{12} .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 2x+5=\pm\sqrt{4\cdot3} \\\\ 2x+5=\pm\sqrt{(2)^2\cdot3} \\\\ 2x+5=\pm2\sqrt{3} .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 2x=-5\pm2\sqrt{3} \\\\ x=\dfrac{-5\pm2\sqrt{3}}{2} .\end{array} Hence the solutions are $ x=\left\{ \dfrac{-5-2\sqrt{3}}{2},\dfrac{-5+2\sqrt{3}}{2} \right\} .$
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