To find the value of x, we need to first determine the formula for the sum of the first x odd numbers.

The sum of the first x odd numbers is given by the formula:
Sum = x^2

So, we have:
1 + 3 + 5 + 7 + 9 +...+ (2x - 1) = x^2

Now, we can substitute the given sum of 400 into the equation:
1 + 3 + 5 + 7 + 9 +...+ (2x - 1) = 400
x^2 = 400

Taking the square root of both sides:
x = √400
x = 20

Therefore, the value of x is 20.