Find all solutions

Question

|x-10|=x^2-10x

Answer 1

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              (except for this note)

Answer 2

lx-10l=x^2-10x

x-10=x^2-10x

x^2-10x-x+10=0

x^2-11x+10=0

factor

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

x-10=0

x=10 is a solution

x-1=0

x=1 is not a solution because l1-10l=l-9l=9 but the right side is equal to -9

-(x-10)=x^2-10x

-x+10=x^2-10x

x^2-10x+x-10=0

x^2-9x-10=0

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

x-10=0

x=10 is a solution as we know

x+1=0

x=-1 is a solution

10 and -1 are the solutions