(x + 1) + (x + 3) + (x + 5) + ... + (x + 99) = 0
=> (x + x + x + ... + x + x) + (1 + 3 + 5 + ... + 97 + 99) = 0
=> \(x.\left(\frac{99-1}{2}+1\right)+\left(\frac{99-1}{2}+1\right).\frac{99+1}{2}=0\)
=> x . 50 + 50 . 50 = 0
=> 50 . (x + 50) = 0
=> x + 50 = 0
=> x = -50