Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.7 - Equations - Exercise Set: 58

Answer

$\left\{-10, -1\right\}$

Work Step by Step

Move all terms to the left side. Note that when a term moves to the other side of the equation, the sign changes to its opposite. $x^2+11x+10=0$ With a leading coefficient of $1$, factor the trinomial by looking for factors of the constant term $(10)$ whose sum is equal to the coefficient of the middle term $(11)$. Note that $10=(10)(1)$ and $10+1 = 11$. This means that the factors of the trinomial are $x+10$ and $x+1$. Thus, the factored form of the trinomial is: $(x+10)(x+1)=0$ Equate each factor to zero then solve each equation to obtain: $x+10 = 0 \text{ or } x+1=0 \\x=-10 \text{ or } x=-1$ The solution set of the given equation is $\left\{-10, -1\right\}$.
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