# Bisection Method Example: Hand Solution and Python Code

Find the solution of the following equation using the bisection method: Write a Python 3 code for this method.

Solution

Hand Solution

Let’s choose the initial values of x so that have different signs: Plugging the above values into the equation, we get: The next value of x is: value into the equation: As the signs of are the same, we will replace the x0 value with x2 and repeat the above steps:  Now, we will replace the x1 value with x2, as the signs of are the same:  As the root of the equation is approximately equal to 1.89282.

Python 3 Code

Let’s define a function for our equation first: Now, we will write a function for defining the sign:  This is our main function for finding the root of the equation. As we must choose two initial values for x, our function should accept two initial parameters: For simplification: And let’s repeat the above steps in a while loop. In order to prevent infinite loop, it’s important to add an exit condition. In our case we will check if the absolute value of y is larger than the 0.001 threshold. To decide what x value should be replaced, the sign check statement will be written as follows: At last, the found x value is returned: The entire code:   The bisection method is one of the root-finding methods for continuous functions. If you want to become an expert at mathematics, you should carefully check our bisection method example and learn more about it.

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