College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 1 - Equations and Inequalities - Exercise Set 1.5 - Page 160: 49


$x=1-\sqrt 3, 1+\sqrt 3$

Work Step by Step

To complete the square, add a term that is the square of half the coefficient of $x$ to both sides of the equation, and factor the left side. Then use the square root property to simplify both sides, and then isolate $x$. $x^2-2x=2$ $(\frac{-2}{2})^2=(-1)^2$ $x^2-2x+(-1)^2=2+(-1)^2$ $x^2-2x+1=2+1$ $x^2-2x+1=3$ $(x-1)^2=\sqrt 3$ $x-1=±\sqrt 3$ $x=1±\sqrt 3$ $x=1-\sqrt 3, 1+\sqrt 3$
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