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: 51


$x=3-2\sqrt 5,3+2\sqrt 5$

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 $x$. $x^2-6x-11=0$ $(\frac{-6}{2})^2=(-3)^2$ $x^2-6x-11+11+(-3)^2=11+(-3)^2$ $x^2-6x+(-3)^2=11+(-3)^2$ $x^2-6x+9=11+9$ $x^2-6x+9=20$ $(x-3)^2=20$ $x-3=±\sqrt {20}$ $x=3±2\sqrt 5$ $x=3-2\sqrt 5,3+2\sqrt 5$
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