How do you solve #x+2=e^(x) #?
Use Newton's Method
You cannot solve the equation using algebraic methods. For this type of equation, I use a numerical analysis technique called Newton's Method.
Here is a reference to Newton's method
You start with a guess for
You do computation, feeding each step back into the equation, until the number that you get doesn't change from the previous number.
Because Newton's Method is computationally intensive, I use an Excel Spreadsheet.
- Open an Excel Spreadsheet
Into cell A1 enter your guess for
Into cell A2 enter the following expression:
=A1 - (EXP(A1) - A1 - 2)/(EXP(A1) - 1)
Copy the contents of cell A2 into the clipboard and then paste it into cell A3 through A10.
You will see that the number quickly converges on
Edit: After reading a very nice comment from Shell. I decided to find the second root by changing the value of cell A1 from 1 to -1. The spreadsheet quickly converges on the value
This question cannot be solved algebraically. Graphing gives
The left side of the equation
The right side of the equation
This equation cannot be solved algebraically but it can be solved graphically.
To solve, plot both