Goal seeking, also known as inverse problem solving, is a process where a problem solver tries to determine the input values of a mathematical expression when the output value is already known. It can be best understood in contrast with direct problem solving, where the goal is to solve a problem by computing the resulting output given a set of input values. When using goal seeking, the inputs are unknown, and the goal is to find the one missing input that solves the problem.

The goal seeking process can be used to solve a variety of problems, ranging from the simple to the complex. In finance and economics, goal seeking is often used to determine the value of a financial asset or investment based on the expected rate of return, or to determine the price of an asset based on its expected returns. In general business, goal seeking can be used to determine the optimal level of production or cost of a product based on the expected demand and prices. Goal seeking can also be used in engineering to determine the necessary force applied on a mechanism to achieve a specific movement, or in computer science to determine the amount of time required to solve a problem.

In most cases, goal seeking can be calculated by hand, however this can be a time-consuming process. To make the process easier, specialized software has been created to automate the task. This type of software usually features a goal seek function which allows the user to enter an output value which the software then takes and finds the necessary input value that corrects the expression. Goal seek software is available both commercially and as open source, making it a versatile and reliable tool for solving problems. It is important to note, however, that goal seek software only works if the expression only has one input value, as it is unable to locate a unique solution in the face of multiple unknowns.

In conclusion, goal seeking is an invaluable problem-solving technique used in a variety of domains, including finance, economics, general business, engineering, and computer science. It involves the task of finding the one missing input value of an expression when the output is already known. While this can be done by hand, specialized goal seek software is available to make the process easier and faster. With this software, however, it is important to remember that it can only be used to solve problems which have one unknown input value.