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: 22


$x=-\frac{8}{3} \text{ and } x=-\frac{16}{3}$

Work Step by Step

Factor the trinomial: $$(x+4)(x+4)=\frac{16}{9}\\ (x+4)^2=\frac{16}{9}$$ Take the square root of both sides: \begin{align*} \sqrt{(x+4)^2}&=\pm \sqrt{\frac{16}{9}}\\\\ x+4&=\pm \sqrt{\frac{4}{3} \cdot \frac{4}{3}}\\\\ x+4&=\pm \frac{4}{3} \end{align*} Subtract $4$ from each side: \begin{align*} x&=\pm \frac{4}{3} -4 \end{align*} Thus, the solutions are: \begin{align*} x_1&=\frac{4}{3}-4\\\\ &=\frac{4}{3}-\frac{12}{3}\\\\ &=-\frac{8}{3} \end{align*} \begin{align*} x_2&=-\frac{4}{3}-4\\\\ &=-\frac{4}{3}-\frac{12}{3}\\\\ &=-\frac{16}{3} \end{align*}
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