Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 4 - Quadratic Functions - 4.6 Solving Quadratic Equations by Using the Quadratic Formula - 4.6 Exercises - Page 373: 39

Answer

$w\approx5.93$, $w\approx2.07$

Work Step by Step

$33=-7(4-w)^2+59$ $-7(4-w)^2+59=33$ $-7(4-w)^2=33-59$ $-7(4-w)^2=-26$ $7(4-w)^2=26$ $7(4^2+w^2-8w)=26$ $7(16+w^2-8w)=26$ $112+7w^2-56w-26=0$ $7w^2-56w+86=0$ $aw^2+bw+c=0$ $a=7,b=-56,c=86$ $w=\frac{56 \pm \sqrt {(-56)^2-4\times7\times86}}{2\times7}$ $w=\frac{56 \pm 2\sqrt {182}}{2\times7}$ $w=2[\frac{28 \pm \sqrt {182}}{2\times7}]$ $w=\frac{28 \pm \sqrt {182}}{7}$ $w\approx5.93$, $w\approx2.07$
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