Solve: x - 2√x) - 2 = 0

Solve: x - 2√x) - 2 = 0
Please show me how you solved it

x - 2√x) - 2 = 0

x - 2 = 2√x (both sides ^2) and we know x ≥ 2.

x^2 - 4x + 4 = 4x

x^2 - 8x + 4 = 0

x = 4 + 2√3

x = 4 - 2√3 (rejected)

x - 2√x - 2 = 0
x - 2 = 2√x
(x-2)^2 = (2√x)^2
x^2 -2x -2x +4 = 4x
x^2 -4x -4x + 4 = 0
x^2 -8x +4 = 0
(x - 4)^2 -12 = 0
(x - 4)^2 = 12
(x - 4) = √12
x = 4 + √12
x = 4 + √(3*4)
x = 4 + 2√3
x = 2(2+√3)

Be careful about the sign!