Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set: 40

Answer

$p=\dfrac{3}{4}\pm\dfrac{\sqrt{5}}{4}$

Work Step by Step

$\Big(p-\dfrac{1}{2}\Big)^{2}=\dfrac{p}{2}$ Evaluate the power on the left side of the equation: $p^{2}-p+\dfrac{1}{4}=\dfrac{p}{2}$ Multiply the whole equation by $4$ to avoid working with fractions: $4\Big(p^{2}-p+\dfrac{1}{4}=\dfrac{p}{2}\Big)$ $4p^{2}-4p+1=2p$ Take all terms to the left side: $4p^{2}-4p-2p+1=0$ Simplify the equation by combining like terms: $4p^{2}-6p+1=0$ Use the quadratic formula to solve this equation. The formula is $p=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=4$, $b=-6$ and $c=1$. Substitute: $p=\dfrac{-(-6)\pm\sqrt{(-6)^{2}-4(4)(1)}}{2(4)}=\dfrac{6\pm\sqrt{36-16}}{8}=...$ $...=\dfrac{6\pm\sqrt{20}}{8}=\dfrac{6\pm2\sqrt{5}}{8}=\dfrac{3}{4}\pm\dfrac{\sqrt{5}}{4}$
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