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 565: 38



Work Step by Step

$4p^2-40p+56=0$ or, $4p^2-40p=-56$ or, $p^2-10p=-14$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-10$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-10)^2}{4}=25$ To complete the square, add $\dfrac{49}{4}$ on both sides. $p^2-10p+25=-14+25$ $\implies (p-5)^2=11$ $\implies (p-5)=3.32$ and $\implies (p-5)=-3.32$ or, $z=1.68,8.32$
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