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

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 3 - Quadratic Functions - Exercises for Skills for Completing the Square - Page 138: 29



Work Step by Step

Completing the square to solve the equation, we find: $$ 5\left(p^2+\frac{9p}{5}-\frac{1}{5}+\left(\frac{9}{10}\right)^2-\left(\frac{9}{10}\right)^2\right) \\ 5\left(\left(p+\frac{9}{10}\right)^2-\frac{1}{5}-\left(\frac{9}{10}\right)^2\right) \\ 5\left(p+\frac{9}{10}\right)^2-\frac{101}{20} \\ \left(p+\frac{9}{10}\right)^2=\frac{101}{100} \\ p=\frac{\sqrt{101}-9}{10},\:p=\frac{-\sqrt{101}-9}{10}$$
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