..............k2=4+2k

Question

k²=4+2k

Answer 1

k² = 4 + 2k                 Given

k² - 2k = 4                  Subtract 2k from each side

k² - 2k + 1 = 4 + 1      Add (b/(2a))² to each side.  In this case, it is 1

k² - 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