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: 48

Answer

The solution set is $\left\{5, 7\right\}$.

Work Step by Step

Simplify the left side to obtain: $x(x)-x(12)=-35 \\x^2-12x=-35$ Add $35$ to both sides of the equation to obtain: $x^2-12x+35=0$ Factor the trinomial by looking for the factors of $35$ whose sum is equal to the coefficient of the middle term ($-12$). These factors are $-7$ and $-5$. This means that the factored form of the trinomial is $(x-7)(x-5)$. Thus, $x^2-12x+35=0 \\(x-7)(x-5)=0$ Equate each factor to 0; then simplify to obtain: $x-7=0 \text{ or } x-5=0 \\x=7 \text{ or } x=5$ The solution set is $\left\{5, 7\right\}$.
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