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: 40



Work Step by Step

$4p^2-40p+56=0$ or, $2p^2-15p+8=43$ or, $p^2-\frac{15}{2}p+4=\frac{43}{2}$ 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, $c=\dfrac{b^2}{4a}=\dfrac{(-\frac{15}{2})^2}{4}=\dfrac{225}{16}$ To complete the square, add $\dfrac{49}{4}$ on both sides. $p^2-\frac{15}{2}p+4+\dfrac{225}{16}=\frac{43}{2}+\dfrac{225}{16}$ $\implies (p-\dfrac{15}{4})^2=\dfrac{505}{16}$ $\implies (p-\dfrac{15}{4})^2=31.57$ $\implies (p-3.75)^2=31.57$ $\implies (p-3.75)=5.62$ and $\implies (p-3.75)=-5.62$ or, $p=9.37,-1.87$
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