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: 16



Work Step by Step

$a^2-2a-35=0$ or, $a^2-2a=35$ Comparing 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 $4$ on both sides. $a^2-2a+1=35+1$ $\implies (a-1)^2=36$ $\implies a-1=6$ and $\implies a-1=-6$ or, $a=7,-5$
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