The required values of x are 1/10 and 1/10.

Given

$$\rm 100x^2 - 20x + 1 = 0$$

$$\rm 100 x^2 - (10 + 10)x + 1 = 0$$

$$\rm 100x^2 - 10x - 10x + 1 = 0$$

$$\rm 10x (10x - 1) - (10x - 1) = 0$$

$$\rm (10x - 1)(10x - 1) = 0$$

$$\rm (10x - 1)^2 = 0$$

$$\rm (10x - 1) = 0$$

$$\rm 10 x = 1$$

$$\rm \therefore x = \frac{1}{10}$$