College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises - Page 112: 23



Work Step by Step

The two numbers whose product is $ac= 25(9)=225 $ and whose sum is $b= 30 $ are $\{ 15,15 \}$. Using these two numbers to decompose the middle term of the given equation, $ 25x^2+30x+9=0 ,$ results to \begin{array}{l}\require{cancel} 25x^2+15x+15x+9=0 \\\\ (25x^2+15x)+(15x+9)=0 \\\\ 5x(5x+3)+3(5x+3)=0 \\\\ (5x+3)(5x+3)=0 .\end{array} Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are \begin{array}{l}\require{cancel} 5x+3=0 \\\\ 5x=-3 \\\\ x=-\dfrac{3}{5} ,\\\\\text{OR}\\\\ 5x+3=0 \\\\ 5x=-3 \\\\ x=-\dfrac{3}{5} .\end{array} Hence, the solution is $ x=-\dfrac{3}{5} .$
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