College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Cumulative Review - Page 196: 4


$\color{blue}{x=\left\{1+\sqrt3, 1-\sqrt3\right\}}$

Work Step by Step

Add $2$ to both sides: $x^2-2x-2+2=0+2 \\x^2-2x=2$ Complete the square by adding $(\frac{-2}{2})^2=1$ to both sides: $x^2-2x+1=2+1 \\x^2-2x+1=3$ Factor the trinomial: $(x-1)^2= 3$ Take the square root of both sides: $\sqrt{(x-1)^2}=\pm\sqrt{3} \\x-1=\pm\sqrt{3}$ Add $1$ to both sides of the equation: $x-1+1=1\pm\sqrt3 \\x=1\pm \sqrt3$ Thus, the solutions are: $\color{blue}{x=\left\{1+\sqrt3, 1-\sqrt3\right\}}$
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