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2. Solution in radicals - Wikipedia

   en.wikipedia.org/wiki/Solution_in_radicals

   A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula

3. Equation solving - Wikipedia

   en.wikipedia.org/wiki/Equation_solving

   Instantiating a symbolic solution with specific numbers gives a numerical solution; for example, a = 0 gives (x, y) = (1, 0) (that is, x = 1, y = 0), and a = 1 gives (x, y) = (2, 1). The distinction between known variables and unknown variables is generally made in the statement of the problem, by phrases such as "an equation in x and y ", or ...

4. Extraneous and missing solutions - Wikipedia

   en.wikipedia.org/wiki/Extraneous_and_missing...

   One of the basic principles of algebra is that one can multiply both sides of an equation by the same expression without changing the equation's solutions. However, strictly speaking, this is not true, in that multiplication by certain expressions may introduce new solutions that were not present before. For example, consider the following ...

5. Theory of equations - Wikipedia

   en.wikipedia.org/wiki/Theory_of_equations

   Simultaneous linear equations: The general theoretical solution was provided by Gabriel Cramer in 1750. However devising efficient methods to solve these systems remains an active subject of research now called linear algebra. Finding the integer solutions of an equation or of a system of equations.

6. Relaxation (iterative method) - Wikipedia

   en.wikipedia.org/wiki/Relaxation_(iterative_method)

   Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [2] [3] [4] Iterative relaxation of solutions is commonly dubbed smoothing because with certain equations, such as Laplace's equation, it resembles repeated application of a local smoothing ...

7. Cramer's rule - Wikipedia

   en.wikipedia.org/wiki/Cramer's_rule

   In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one column by the ...