Solution of Equation

The solution of an equation is the set of all values which, when substituted for unknowns, make an equation true. For equations having one unknown, raised to a single power, two fundamental rules of algebra, including the additive property and the multiplicative property, are used to determine its solutions. Solutions for equations with multiple unknown variables are found by using the principles for a system of equations. Equations with terms raised to a power greater than one can be solved by factoring and, in some specific cases, by the quadratic equation.

The idea of a solution of equations has existed since the time of the Egyptians and Babylonians. During these times, they used simple algebraic methods to determine solutions for practical problems related to their everyday life. The methods used by the ancients were preserved in a treatise written by the Arabian mathematician Al-Kowarizmi (A.D. 825). In this work, he includes methods for solving linear equations as well as second degree equations. Solutions for some higher degree equations were worked out during the sixteenth century by an Italian mathematician named Gerolamo Cardano (1501-1576).