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: 45


The solution set is $\left\{-12, 1\right\}$.

Work Step by Step

Add $-12$ to both sides of the equation to obtain: $x^2+11x-12=0$ Factor the trinomial by looking for the factors of $-12$ whose sum is equal to the coefficient of the middle term ($11$). These factors are $-1$ and $12$. This means that the factored form of the trinomial is $(x-1)(x+12)$. Thus, $x^2+11x-12=0 \\(x-1)(x+12)=0$ Equate each factor to 0; then, solve each equation to obtain: $x-1=0 \text{ or } x+12=0 \\x=1 \text{ or } x=-12$ The solution set is $\left\{-12, 1\right\}$.
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