College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises - Page 112: 20


$x=\left\{ -8,8 \right\}$

Work Step by Step

Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of two squares, the factored form of the given expression, $ x^2-64=0 ,$ is \begin{array}{l}\require{cancel} (x-8)(x+8)=0 .\end{array} Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are \begin{array}{l}\require{cancel} x-8=0 \\\\ x=8 ,\\\\\text{OR}\\\\ x-8=0 \\\\ x=8 .\end{array} Hence, the solutions are $ x=\left\{ -8,8 \right\} .$
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