X的平方减二X减X减1的绝对值减1等于零
x²-2x-|x-1|-1=0
x²-2x+1-|x-1|-2=0
(x-1)²-|x-1|-2=0
|x-1|²-|x-1|-2=0
令|x-1|=t>=0
∴t²-t-2=0
(t-2)(t+1)=0
∴t=2,t=-1舍去
∴|x-1|=2
x-1=2或x-1=-2
x=3或x=-1