To solve this equation, we can use the formula for the sum of an arithmetic series:

S = (n/2)(2a + (n-1)d)

where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, the first term is x+1, the common difference is 1, and the number of terms is 37.

So, we have:

499 = (37/2)(2(x+1) + (37-1)(1))

Simplifying the equation:

499 = (37/2)(2x + 2 + 36)

499 = (37/2)(2x + 38)

Dividing both sides by (37/2):

499 / (37/2) = 2x + 38

Simplifying the left side:

(499 * 2) / 37 = 2x + 38

998 / 37 = 2x + 38

26.97 = 2x + 38

Subtracting 38 from both sides:

26.97 - 38 = 2x

-11.03 = 2x

Dividing both sides by 2:

-11.03 / 2 = x

x = -5.515

Therefore, the value of x is approximately -5.515.