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: 22



Work Step by Step

$p^2+5p-7=0$ or, $p^2+5p=7$ 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. $p^2+5p+\dfrac{25}{4}=7+\dfrac{25}{4}$ $\implies (p+\dfrac{5}{2})^2=\dfrac{53}{4}$ $\implies (p+\dfrac{5}{2})=3.64$ and $\implies (p+\dfrac{5}{2})=-3.64$ or, $p=1.14,-6.14$
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