Let's simplify the equation step by step:

Expand the left side of the equation:
(х+1)^2 = x^2 + 2x + 1

Expand the right side of the equation:
(1-x^2)/2 = (1/2) - (x^2/2)

Rewrite the equation with the expanded terms:
x^2 + 2x + 1 - (1/2) + (x^2/2) = 4

Combine like terms:
x^2 + x + (2/2) - (1/2) = 4
x^2 + x + 1/2 = 4

Subtract 1/2 from both sides of the equation:
x^2 + x = 4 - 1/2
x^2 + x = 7/2

Therefore, the simplified form of the equation is x^2 + x = 7/2.