Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set - Page 323: 69


The numbers are either: $6$ and $11$ or $-11$ and $-6$

Work Step by Step

Let $x$=smaller number $x+5$=bigger number The product of the two numbers is 66 so $\\x(x+5)=66 \\x^2+5x=66 \\x^2+5x-66=0$ The factors of $-66$ whose sum is equal to the middle term's coefficient are 11 and $-6$. Thus, the factored form of the trinomial is: $\\(x+11)(x-6)=0$ Equate each factor to zero then solve each equation to have: $\\x+11=0 \text{ or } x-6=0 x=-11 \text{ or } x=6$ Therefore the possible values of the numbers are: $\\6$ and $11$ or $-11$ and $-6$
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