Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 552: 151

Answer

$\{-5,2\}$.

Work Step by Step

The given equation is $\Rightarrow 26-11x=16-8x+x^2$ Add $-26+11x$ to both sides. $\Rightarrow 26-11x-26+11x=16-8x+x^2-26+11x$ Simplify. $\Rightarrow 0=x^2+3x-10$ Rewrite the middle term $3x$ as $5x-2x$. $\Rightarrow 0=x^2+5x-2x-10$ Group the terms. $\Rightarrow 0=(x^2+5x)+(-2x-10)$ Factor each group. $\Rightarrow 0=x(x+5)-2(x+5)$ Factor out $(x+5)$. $\Rightarrow 0=(x+5)(x-2)$ By using zero product rule set each factor equal to zero. $\Rightarrow x+5=0$ or $x-2=0$ Isolate $x$. $\Rightarrow x=-5$ or $x=2$ The solution set is $\{-5,2\}$.
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