Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 565: 36



Work Step by Step

$w^2+7w-40=0$ or, $w^2+7w=40$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=7$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(7)^2}{4}=\dfrac{49}{4}$ To complete the square, add $\dfrac{49}{4}$ on both sides. $w^2+7w+\dfrac{49}{4}=40+\dfrac{49}{4}$ $\implies (w+\dfrac{7}{2})^2=\dfrac{209}{4}$ $\implies (w+3.5)^2=52.25$ $\implies (w+3.5)=7.23$ and $\implies (w+3.5)=-7.23$ or, $w=3.73,-10.73$
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