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: 32


The solution set is $\left\{-5, -4\right\}$.

Work Step by Step

Factor the trinomial by looking for the factors of 20 whose sum is equal to the coefficient of the middle term (9). These factors are 4 and 5. This means that the factored form of the trinomial is $(x+4)(x+5)$. Thus, $x^2+9x+20=0 \\(x+4)(x+5)=0$ Equate each factor to 0 then solve each equation to obtain: $x+4=0 \text{ or } x+5=0 \\x=-4 \text{ or } x=-5$ The solution set is $\left\{-5, -4\right\}$.
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