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: 29



Work Step by Step

$3r^2+18r=21$ Re-write the equations as: $r^2+6r=7$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=6$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(6)^2}{4}=9$ To complete the square, add $9$ on both sides. $r^2+6r+9=7+9$ $\implies (r+3)^2=16$ $\implies r+3=4$ and $\implies r+3=-4$ or, $r=1,-7$
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