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: 50

Answer

The solution set is $\left\{-2, 8\right\}$.

Work Step by Step

Multiply $-1$ on both sides of the equation to obtain: $x^2-6x-16=0$ Factor the trinomial by looking for the factors of $-16$ whose sum is equal to the coefficient of the middle term ($-6$). These factors are $-8$ and $2$. This means that the factored form of the trinomial is $(x-8)(x+2)$. Thus, $x^2-6x-16=0 \\(x-8)(x+2)=0$ Equate each factor to 0; then simplify to obtain: $x-8=0 \text{ or } x+2=0 \\x=8 \text{ or } x=-2$ The solution set is $\left\{-2, 8\right\}$.
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