Verified answer

f(x) = x² + 2x + 3

f(z + 2) = (z + 2)² + 2(z + 2) + 3 = z² + 4z + 4 + 2z + 4 + 3 = z² + 6z + 11

f(z - 2) = (z - 2)² + 2(z - 2) + 3 = z² - 4z + 4 + 2z - 4 + 3 = z² - 2z + 3

f(z + 2) = f(z - 2) + 4

z² + 6z + 11 = z² - 2z + 3 + 4

z² + 6z - z² + 2z = 7 - 11

8z = - 4

z = - 0,5