Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 579: 28



Work Step by Step

$4w^2+12w-44=0$ or, $4w^2+12w=44$ Rewrite the equation as: $w^2+3w=11$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=3$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(3)^2}{4}=\dfrac{9}{4}$ To complete the square, add $\dfrac{9}{4}$ on both sides. $w^2+3w+\dfrac{9}{4}=11+\dfrac{9}{4}$ $\implies (w+\dfrac{9}{4})^2=13.25$ $\implies (w+\dfrac{9}{4})=3.64$ and $\implies (w+\dfrac{9}{4})=-3.64$ or, $w=2.14,-5.14$
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