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: 37

Answer

The solution set is $\left\{-9, 4\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of $-36$ whose sum is equal to the coefficient of the middle term ($5$). These factors are $-4$ and $9$. This means that the factored form of the trinomial is $(n-4)(n+9)$. Thus, $n^2+5n-36=0 \\(n-4)(n+9)=0$ Equate each factor to 0; then, solve each equation to obtain: $n-4=0 \text{ or } n+9=0 \\n=4 \text{ or } n=-9$ The solution set is $\left\{-9, 4\right\}$.
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