Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Cumulative Review - Page 334: 49


$x=-5 \text{ or } x=\frac{1}{2}$

Work Step by Step

There is a need to factor the trinomial on the left side of the equation. The product of the leading term (2) and the constant term (-5) is $-10$. The factors of $-10$ whose sum is equal to the coefficient of the middle term, which is 9, are $10$ and $-1$. Write the middle using these factors to have: $\\2x^2+10x-x-5=0$ Regroup to have: $\\(2x^2+10x)+(-x-5)=0$ Factor out the GCF of each group to have: $\\2x(x+5)+(-1)(x+5)=0 \\(x+5)(2x-1)=0$ Equate each factor to zero then solve each equation to have: $\\x+5=0 \text{ or } 2x-1=0 \\x=-5 \text{ or } 2x=1 \\x=-5 \text{ or } x=\frac{1}{2}$
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