Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.4 Quadratic Equations - 1.4 Exercises: 41

Answer

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

Work Step by Step

Add $2$ to both sides: $x-2x=2$ Add the square of one-half of the coefficient of $x$, which is $(\frac{-2}{2})^2=(-1)^2=1$, to obtain: $x^2-2x+1=2+1 \\(x-1)^2=3$ Take the square root of both sides to obtain: $\sqrt{(x-1)^2}=\pm \sqrt{3} \\x-1 = \pm \sqrt3$ Add $1$ to both sides: $x=1 \pm \sqrt3$ Thus, the solution set is: $\color{blue}{\left\{1-\sqrt3, 1+\sqrt3\right\}}$.
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