Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-6 Complete the Square - Practice and Problem-Solving Exercises - Page 237: 25


$\left\{-\dfrac{4}{5}, \dfrac{2}{5}\right\}$

Work Step by Step

Factor the trinomial to obtain: \begin{align*} (5x+1)(5x+1)&=9\\ (5x+1)^2&=3^2 \end{align*} Take the square root of both sides: \begin{align*} \sqrt{(5x+1)^2}&=\pm\sqrt{3^2}\\\\ 5x+1&=\pm3\\\\ 5x&=-1\pm 3\\\\ \frac{5x}{5}&=\frac{-1\pm3}{5}\\\\ x&=-\frac{1}{5} \pm \frac{3}{5} \end{align*} Split the solutions to obtain: \begin{align*} x_1&=-\frac{1}{5}-\frac{3}{5}\\ &=-\frac{4}{5} \end{align*} \begin{align*} x_2&=-\frac{1}{5}+\frac{3}{5}\\ &=\frac{2}{5} \end{align*}
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