complex numbers

x² + x + 2x√(x + 2) = 14
[x + √(x + 2)]² - 2 = 14
[x + √(x + 2)]² = 16
x + √(x + 2) = 4 or x + √(x + 2) = 4

When x + √(x + 2) = 4:
√(x + 2) = 4 - x
[√(x + 2)]² = [4 - x]²
x + 2 = 16 - 8x + x²
x² - 9x + 14 = 0
(x - 2)(x - 7) = 0
x = 2 or x = 7 (rejected)

When x + √(x + 2) = -4:
√(x + 2) = -4 - x
[√(x + 2)]² = [-4 - x]²
x + 2 = 16 + 8x + x²
x² + 7x + 14 = 0
Determinant Δ = (7)² - 4(1)(14) = -7 < 0
There is no real root.

Ans: x = 2