Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 100 ;b = - 20 ;c = 1

= 100.1 = 100

And either of their sum or difference = b

= - 20

Thus the two terms are - 10 and - 10

Sum = - 10 - 10 = - 20

Product = - 10. - 10 = 100

10x(10x-1)-1(10x-1) = 0

(10x-1)(10x-1) = 0

(10x-1) = 0 or (10x-1) = 0

Roots of equation are repeated