## Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley

# Chapter 3 - Quadratic Functions - Exercises for Skills for Completing the Square - Page 138: 28

#### Answer

$$r=\frac{\sqrt{177}+3}{14},\:r=\frac{-\sqrt{177}+3}{14}$$

#### Work Step by Step

Completing the square to solve the equation, we find: $$7\left(\left(r-\frac{3}{14}\right)^2-\frac{6}{7}-\left(-\frac{3}{14}\right)^2\right) \\ 7\left(r-\frac{3}{14}\right)^2-\frac{177}{28} \\ \left(r-\frac{3}{14}\right)^2=\frac{177}{196} \\ r=\frac{\sqrt{177}+3}{14},\:r=\frac{-\sqrt{177}+3}{14}$$

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