College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.2 - Quadratic Equations - 1.2 Assess Your Understanding: 20


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

Work Step by Step

Factor out the GCF (which is 2) on the left side to obtain: $2(y^2-25)=0 \\2(y^2-5^2)=0$ Factor the difference of two squares using the formula $a^2-b^2=(a-b)(a+b)$ to obtain: $2(y-5)(y+5)=0$ Use the Zero-Product Property by equating each factor with a variable to zero to obtain: $\begin{array}{ccc} &y-5=0 &\text{ or } &y+5=0 \\&y=5 &\text{ or } &y=-5 \end{array}$ Therefore the solution set is $\left\{-5, 5\right\}$.
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