Given two values of the independent variable, ''x''<sub>0</sub> and ''x''<sub>1</sub>, which are on two different sides of the root being sought, ''<math>f(x_0)f(x_2) < 0''</math>.The method begins by evaluating the function at the midpoint ''x''<sub>1</sub> between the two points. One then finds the unique exponential function of the form ''e''<sup>''ax''</sup> which, when multiplied by ''f'', transforms the function at the three points into a straight line. The false position method is then applied to the transformed values, leading to a new value ''x''<sub>3</sub>, between ''x''<sub>0</sub> and ''x''<sub>2</sub>, which can be used as one of the two bracketing values in the next step of the iteration.
The other bracketing value is taken to be ''x''<sub>3</sub> if f(''x''<sub>3</sub>) has the opposite sign to f(''x''<sub>4</sub>), or otherwise whichever of ''x''<sub>1</sub> and ''x''<sub>2</sub> has f(x) of opposite sign to f(''x''<sub>4</sub>).
