Equations

Again, an equation is formed when a function is assigned the value 0 and we are asked to find the values of the function input, normally x, that satisfy the equation. These values are called the roots of the original function. The process of finding these values is called solving an equation, which is a rich topic in mathematics and, specifically, algebra.

In this section, we will discuss two fundamental methods of solving equations by hand as well as examine the available computational tools in Python to facilitate the process of automatically solving equations. We will start with the first method, algebraic manipulations.

Algebraic Manipulations

While we are classifying this as a method, algebra is, in general, a technique to translate an equation to a simpler form so that solutions can be found easily. Some typical ways to translate an equation are adding/subtracting a constant to both sides of the equation, multiplying/dividing both sides by a non-zero constant...