Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - Chapter 6 Review Problem Set: 30

Answer

$\left\{-\frac{5}{4}\right\}$

Work Step by Step

The equation can be written as: $(4y)^2+2(4y)(5) + 5^2=0$ The left side of the equation is a perfect square trinomial of the form $a^2+2ab+b^2$ where $a=4y$ and $b=5$. RECALL: $a^2+2ab+b^2=(a+b)^2$ Factor the trinomial using the formula above with $a=4y$ and $b=5$ to obtain: $(4y+5)^2=0$ Equate the factor to 0 to obtain: $4y+5=0$ Solve the equation to obtain: $4y=-5 \\y=\frac{-5}{4}$ Therefore the solution set is $\left\{-\frac{5}{4}\right\}$.
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