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: 19

Answer

$x=\left\{ -10,10 \right\}$

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^2-100=0 ,$ is \begin{array}{l}\require{cancel} (x-10)(x+10)=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-10=0 \\\\ x=10 ,\\\\\text{OR}\\\\ x+10=0 \\\\ x=-10 .\end{array} Hence, the solutions are $ x=\left\{ -10,10 \right\} .$
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