Solve each of the following equations by using the method of completing the square:

x^{2} - 4x + 1 = 0

Given: x^{2} - 4x + 1 = 0

x^{2} - 4x = - 1

x^{2} - 2.x.2 + 2^{2} = - 1 + 2^{2} (adding 2^{2} on both sides)

(x - 2)^{2} = - 1 + 4 = 3 using a^{2} - 2ab + b^{2} = (a - b)^{2}

(taking square root on both sides)

Hence the roots of equation are

2