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: 39

Answer

$n=3\pm\sqrt{5}$

Work Step by Step

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