SOLUTION: x^-x=1 what is the solution set{ }? quadratic formula.

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Question 236187: x^-x=1 what is the solution set{ }?
quadratic formula.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the given equation.


Subtract 1 from both sides.


Notice that the quadratic is in the form of where , , and


Let's use the quadratic formula to solve for "x":


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


or Break up the expression.


So the solutions are or


which approximate to or

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