 The quadratic equation on a number formula_2 can be solved using the well-known quadratic formula, which can be derived by completing the square.That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated as a decimal fraction only by applying an additional root extraction algorithm.If the roots are real, there is an alternative technique that obtains a rational approximation to one of the roots by manipulating the equation directly.