By completing the square find in terms of k the solutions of the equation x^2 - 4kx + 6 =0?

x² - 4kx + 6 = 0
x² - 4kx = -6
x² - 2(2k)x + (2k)² = -6 + (2k)²
(x - 2k)² = 4k² - 6
x - 2k = ± √(4k² - 6)
x = 2k ± √(4k² - 6)

x² - 4kx + 6 = 0

x² - 4kx = - 6

x² - 4kx + (2k)² - (2k)² = - 6

x² - 4kx + (2k)² = (2k)² - 6

(x - 2k)² = 4k² - 6

x - 2k = ± √(4k² - 6)

x = 2k ± √(4k² - 6)


x₁ = 2k + √(4k² - 6)

x₂ = 2k - √(4k² - 6)