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: 27


\begin{align*}x&=-\frac{10}{3} &\text{and}& &x=\frac{2}{3} \end{align*}

Work Step by Step

Factor the trinomial to obtain: \begin{align*} (3x+4)(3x+4)&=36\\ (3x+4)^2&=6^2 \end{align*} Take the square root of both sides: \begin{align*} \sqrt{3x+4)^2}&=\pm \sqrt{6^2}\\ 3x+4&=\pm 6 \end{align*} Solve for $x$: \begin{align*}3x&=-4\pm 6\\\\ \frac{3x}{3}&=\frac{-4\pm6}{3}\\\\ x&=-\frac{4}{3} \pm 2 \end{align*} Split the solutions to obtain: \begin{align*} x&=-\frac{4}{3}-2\\\\ x_1&=-\frac{4}{3}-\frac{6}{3}\\\\ x_1&=-\frac{10}{3}\\\\ \end{align*} \begin{align*} x&=-\frac{4}{3}+2\\\\ x_1&=-\frac{4}{3}+\frac{6}{3}\\\\ x_1&=\frac{2}{3}\\\\ \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.