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: 30



Work Step by Step

$2v^2-10v-20=8$ Re-write the equations as: $v^2-5v-10=4$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-5$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-5)^2}{4}=\dfrac{25}{4}$ To complete the square, add $\dfrac{25}{4}$ on both sides. $v^2-5v-10+\dfrac{25}{4}=4+\dfrac{25}{4}$ $\implies (v-\dfrac{5}{2})^2=\dfrac{81}{4}$ $\implies (v-\dfrac{5}{2})= \dfrac{9}{2}$ and $\implies (v-\dfrac{5}{2})= -\dfrac{9}{2}$ or, $v=7,-2$
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