Factor the polynomial completely.
t^2 + 20t +100
The coefficient of t² being unity (1), we only have to look at the factors of the constant term, namely 100.
100=2*2*5*5
Possible factor combinations are:
2*50
4*25
5*20
10*10
the last of which add up to 20, coefficient for t.
Thus
t² + 20t + 100
=(x+10)(x+10)