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 564: 25



Work Step by Step

$4a^2-8a=24$ Rewrite the equation as: $a^2-2a=6$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-2$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-2)^2}{4}=1$ To complete the square, add $1$ on both sides. $a^2-2a+1=6+1$ $\implies (a-1)^2=7$ $\implies a-1=2.65$ and $\implies a-1=-2.65$ or, $a=3.65,-1.65$
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