SOLUTION: Find all solutions of the equation|x^2-20x-1|=20. Please explain in detail!

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Question 1167038: Find all solutions of the equation|x^2-20x-1|=20. Please explain in detail!
Answer by ikleyn(52876) About Me  (Show Source):
You can put this solution on YOUR website!
.

It means EITHER

     x^2 - 20x - 1 = 20

OR

     x^2 - 20x - 1 = -20.


Case 1) :   x^2 - 20x - 1 = 20.


     Then  x^2 - 20x - 21 = 0.

     Factor left side  (x-20)*(x+1) = 0

     giving the roots  x= 20  and  x= -1.



Case 2) :   x^2 - 20x - 1 = -20.


     Then  x^2 - 20x + 19 = 0.

     Factor left side  (x-19)*(x-1) = 0

     giving the roots  x= 19  and  x= 1.


ANSWER.  There are 4 solutions  x= -1, 1, 19 and 20.

Solved.

For your better understanding, here the plot is 





Plot y = |x^2 - 20x - 1| (red)  and  y = 20 (green)