How can the equation x^x + x - 1 = 0 be solved analytically?

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In summary, The solution to the equation x^x + x - 1 = 0 is approximately 0.543, which can be found using numerical methods such as Newton's method or the bisection method. There is no general formula for solving this type of equation and graphing the equation may not accurately determine the solution. There is one real solution to the equation, but there are also complex solutions.
  • #1
mnb96
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Hello,
does anyone have a hint on how to solve analytically (if possible) the following equation in x:

[tex]x^x + x -1 = 0[/tex]

Thanks.
 
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  • #2
There is no solution to that in the elementary functions. You will need to use numerical techniques.
 

FAQ: How can the equation x^x + x - 1 = 0 be solved analytically?

What is the solution to the equation x^x + x - 1 = 0?

The solution to this equation is approximately 0.543, according to numerical methods. This is the value of x that makes the equation true.

How do you solve x^x + x - 1 = 0 for x?

This equation cannot be solved algebraically, so numerical methods such as Newton's method or the bisection method must be used to approximate the solution.

Is there a general formula for solving equations of the form x^x + x + c = 0?

No, there is not a general formula for solving this type of equation. Each equation must be solved using numerical methods as there is no algebraic solution.

Can you graph the equation x^x + x - 1 = 0 to find the solution?

Yes, the equation can be graphed, but it is difficult to accurately determine the solution from the graph alone. Numerical methods are more reliable for finding the solution.

Are there any real solutions to the equation x^x + x - 1 = 0?

Yes, there is one real solution to this equation, which is approximately 0.543. However, there are also complex solutions to the equation.

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