Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.3 - Factoring Trinomials of the Form x^2+bx+x - Problem Set 6.3 - Page 255: 42


The solution set is $\left\{-9, 8\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of $-72$ whose sum is equal to the coefficient of the middle term ($1$). These factors are $-8$ and $9$. This means that the factored form of the trinomial is $(t-8)(t+9)$. Thus, $t^2+t-72=0 \\(t-8)(t+9)=0$ Equate each factor to 0; then, solve each equation to obtain: $t-8=0 \text{ or } t+9=0 \\t=8 \text{ or } t=-9$ The solution set is $\left\{-9, 8\right\}$.
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