To solve the equation x^2 - 4x + 1 = 0, we can use the quadratic formula.

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 1, b = -4, and c = 1. Plugging these values into the quadratic formula, we have:

x = (-(-4) ± √((-4)^2 - 4(1)(1))) / (2(1))
x = (4 ± √(16 - 4)) / 2
x = (4 ± √12) / 2
x = (4 ± 2√3) / 2

Simplifying further, we have:

x = 2 ± √3

Therefore, the solutions to the equation x^2 - 4x + 1 = 0 are x = 2 + √3 and x = 2 - √3.