# How do you solve #x+2=e^(x) #?

##### 2 Answers

Use Newton's Method

#### Explanation:

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

Let

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

#### Explanation:

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