k^{2}=4+2k

k^{2} = 4 + 2k Given

k^{2} - 2k = 4 Subtract 2k from each side

k^{2} - 2k + 1 = 4 + 1 Add (b/(2a))^{2} to each side. In this case, it is 1

k^{2} - 2k + 1 = 5 Simplify the right side

(k - 1)^{2} = 5 Factor the left side into a perfect square

k - 1 = +/- sqrt(5) Take the square root of both sides

k = 1 +/- sqrt(5) Add 1 to each side