What is trial and error method?

Substituting different values of the variable and checking the equality of LHS and RHS is the trial and error method. Let us solve the equation 3x + 5 = 17. We start to substitute different values of x. The value for which both the sides are balanced is the required solution.

For x = 4, LHS = RHS. The required solution is x = 4.

Trial and error is a fundamental method of problem-solving. It is characterized by repeated, varied attempts which are continued until success, or until the practicer stops trying. According to W.H. Thorpe, the term was devised by C. Lloyd Morgan (1852–1936) after trying out similar phrases "trial and failure" and "trial and practice". Under Morgan's Canon, animal behaviour should be explained in the simplest possible way. Where behavior seems to imply higher mental processes, it might be explained by trial-and-error learning. An example is a skillful way in which his terrier Tony opened the garden gate, easily misunderstood as an insightful act by someone seeing the final behavior. Lloyd Morgan, however, had watched and recorded the series of approximations by which the dog had gradually learned the response, and could demonstrate that no insight was required to explain it.