Understanding the Problem:
Given equation: |2x - √(2x - 1)²| = 1
We need to find all integral values of x in the interval [-4, 100] that satisfy this equation.

Solution:

1. Break down the Equation:
- The absolute value of a number is always positive. So, the equation can be written as:
2x - √(2x - 1)² = 1 or 2x - √(2x - 1)² = -1

2. Solve for x:
- For 2x - √(2x - 1)² = 1:
2x - (2x - 1) = 1
2x - 2x + 1 = 1
1 = 1 (Always true)
- For 2x - √(2x - 1)² = -1:
2x - (2x - 1) = -1
2x - 2x + 1 = -1
1 = -1 (Not possible)
Hence, the only valid solution is when 2x - √(2x - 1)² = 1.

3. Find Integral Values of x:
- Now, solve 2x - √(2x - 1)² = 1 for integral values of x in the interval [-4, 100].
2x - (2x - 1) = 1
2x - 2x + 1 = 1
1 = 1
So, all integral values of x in the interval [-4, 100] satisfy this equation.

4. Calculate the Sum of Integral Values of x:
- The sum of all integral values of x in the interval [-4, 100] is the sum of numbers from -4 to 100, inclusive.
Sum = (-4 + 100) * (100 - (-4) + 1) / 2
Sum = 96 * 105 / 2
Sum = 5040

5. Calculate a+b+c+d:
- From the sum calculated above, a = 5, b = 0, c = 4, d = 0
Therefore, a + b + c + d = 5 + 0 + 4 + 0 = 9.
So, the sum of all integral values of x in the interval [-4, 100] satisfying the given equation is 5040, and a + b + c + d = 9.