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: 46


The solution set is $\left\{-10, 2\right\}$.

Work Step by Step

Add $-20$ to both sides of the equation to obtain: $x^2+8x-20=0$ Factor the trinomial by looking for the factors of $-20$ whose sum is equal to the coefficient of the middle term ($8$). These factors are $-2$ and $10$. This means that the factored form of the trinomial is $(x-2)(x+10)$. Thus, $x^2+8x-20=0 \\(x-2)(x+10)=0$ Equate each factor to 0; then, solve each equation to obtain: $x-2=0 \text{ or } x+10=0 \\x=2 \text{ or } x=-10$ The solution set is $\left\{-10, 2\right\}$.
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