Let's solve the equation step by step:

Х + (5х + 2) * 2 = 25(1 + х'2)

Expand the expression inside the parentheses:

Х + 10х + 4 = 25(1 + х'2)

Combine like terms on the left side:

11х + 4 = 25(1 + х'2)

Distribute on the right side:

11х + 4 = 25 + 25х'2

Subtract 25 from both sides:

11х - 21 = 25х'2

Subtract 11х from both sides:

-21 = 14х'2

Finally, divide by 14 to solve for x:

x = -21 / 14
x = -3 / 2

Therefore, the solution to the equation is x = -3 / 2.