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: 49

Answer

The solution set is $\left\{-6, 4\right\}$.

Work Step by Step

Multiply $-1$ to both sides of the equation to obtain: $x^2+2x-24=0$ Factor the trinomial by looking for the factors of $-24$ whose sum is equal to the coefficient of the middle term ($-2$). These factors are $-4$ and $6$. This means that the factored form of the trinomial is $(x-4)(x+6)$. Thus, $x^2+2x-24=0 \\(x-4)(x+6)=0$ Equate each factor to 0; then simplify to obtain: $x-4=0 \text{ or } x+6=0 \\x=4 \text{ or } x=-6$ The solution set is $\left\{-6, 4\right\}$.
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