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: 55



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 $x$. $x^2-5x+6=0$ $(\frac{-5}{2})^2$ $x^2-5x+6-6+(\frac{-5}{2})^2=-6+(\frac{-5}{2})^2$ $x^2-5x+(\frac{-5}{2})^2=-6+(\frac{-5}{2})^2$ $x^2-5x+\frac{25}{4}=-6+\frac{25}{4}$ $x^2-5x+\frac{25}{4}=\frac{1}{4}$ $(x-\frac{5}{2})^2=\frac{1}{4}$ $x-\frac{5}{2}=±\frac{1}{2}$ $x=\frac{5}{2}±\frac{1}{2}$ $x=2,3$
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