Squaring both sides of the equation to eliminate the square root, we get:
[4 + 2x - x^2 = (x - 2)^2]
Expanding the right side:
[4 + 2x - x^2 = x^2 - 4x + 4]
Rearranging the terms:
[0 = 2x - 4x + 4 - 2x]
[0 = -3x + 4]
[3x = 4]
[x = \frac{4}{3}]
Therefore, the solution to the equation is x = 4/3.
Squaring both sides of the equation to eliminate the square root, we get:
[4 + 2x - x^2 = (x - 2)^2]
Expanding the right side:
[4 + 2x - x^2 = x^2 - 4x + 4]
Rearranging the terms:
[4 + 2x - x^2 = x^2 - 4x + 4]
[0 = 2x - 4x + 4 - 2x]
[0 = -3x + 4]
[3x = 4]
[x = \frac{4}{3}]
Therefore, the solution to the equation is x = 4/3.