We write, $-20 x=-10 x-10 x$ as $100 x^{2} \times 1=100 x^{2}=(-10 x) \times(-10 x)$

$\therefore 100 x^{2}-20 x+1=0$

$\Rightarrow 100 x^{2}-10 x-10 x+1=0$

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

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

$\Rightarrow(10 x-1)^{2}=0$

$\Rightarrow 10 x-1=0$

$\Rightarrow x=\frac{1}{10}$

Hence, $\frac{1}{10}$ is the repreated root of the given equation.