## To solve this equation, follow these steps:

1. Start by dividing both sides of the equation by 21 to isolate the expression (X-(1/7))^2 on the left side:

(X-(1/7))^2 = (3/7) / 21

Simplifying the right side gives:

(X-(1/7))^2 = 1/49

2. Next, take the square root of both sides to eliminate the squared term on the left side:

sqrt((X-(1/7))^2) = sqrt(1/49)

Simplify by removing the square root and keeping the positive and negative square root solutions:

X-(1/7) = Β±1/7

3. Now, let's solve for X. Start with the positive square root solution:

X-(1/7) = 1/7

Add (1/7) to both sides to isolate X:

X = 1/7 + 1/7

Simplify the right side:

X = 2/7

Thus, the positive square root solution is X = 2/7.

4. Now, let's solve for X using the negative square root solution:

X-(1/7) = -1/7

Add (1/7) to both sides to isolate X:

X = -1/7 + 1/7

Simplify the right side:

X = 0

Thus, the negative square root solution is X = 0.

Therefore, the two solutions to the equation are X = 2/7 and X = 0.