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An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.
Completing the square is the oldest method of solving general quadratic equations, used in Old Babylonian clay tablets dating from 1800–1600 BCE, and is still taught in elementary algebra courses today.
The Japanese mathematician Seki Kōwa used a form of Newton's method in the 1680s to solve single-variable equations, though the connection with calculus was missing. [6] Newton's method was first published in 1685 in A Treatise of Algebra both Historical and Practical by John Wallis. [7]
To solve this kind of equation, the technique is add, subtract, multiply, or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated, the other side of the equation is the value of the variable. [ 37 ]
The algebraic equations are the basis of a number of areas of modern mathematics: Algebraic number theory is the study of (univariate) algebraic equations over the rationals (that is, with rational coefficients). Galois theory was introduced by Évariste Galois to specify criteria for deciding if an algebraic equation may be solved in terms of ...
Algebraic equations can be used to describe geometric figures. All values for and that solve the equation are interpreted as points. They are drawn as a red, upward-sloping line in the graph above. Algebraic equations can be interpreted geometrically to describe spatial figures in the form of a graph.