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:
$n=\dfrac{-(-6)\pm\sqrt{(-6)^{2}-4(1)(4)}}{2(1)}=\dfrac{6\pm\sqrt{36-16}}{2}=...$
$...=\dfrac{6\pm\sqrt{20}}{2}=\dfrac{6\pm2\sqrt{5}}{2}=3\pm\sqrt{5}$