Explanation:

To solve the equation and find the value of ‘x’:

1. Original equation setup:

x² + 1 = (6/7) of 1428 + 2

2. Calculate the right side of the equation:

- Find (6/7) of 1428:

\( \frac{6}{7} \times 1428 = 1224 \)

- Add 2 to the result:

1224 + 2 = 1226

3. Solve for x²:

- Given that x² + 1 = 1226, rearrange to find x²:

x² = 1226 - 1

x² = 1225

4. Find x:

- v1225 = 35

5. Check options:

- Option 1: 1225

- Option 2: 35

- Option 3: v1227

- Option 4: 55

- Option 5: 26

Hence, the correct answer is Option 2: 35.