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The first use of an equals sign, equivalent to 14x + 15 = 71 in modern notation. From The Whetstone of Witte by Robert Recorde of Wales (1557). [1]In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The roots of a polynomial expression of degree n, or equivalently the solutions of a polynomial equation, can always be written as algebraic expressions if n < 5 (see quadratic formula, cubic function, and quartic equation). Such a solution of an equation is called an algebraic solution.
The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).
Parametric equation. The butterfly curve can be defined by parametric equations of x and y. In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. [1] Parametric equations are commonly used to express the coordinates of the points that make up a geometric object ...
Order of operations. In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and ...
For example, is an expression, while is a formula. Expressions can be evaluated or partially evaluated by replacing operations that appear in them with their result. For example, the expression 8 × 2 − 5 {\displaystyle 8\times 2-5} evaluates partially to 16 − 5 {\displaystyle 16-5} and totally to 11. {\displaystyle 11.}
Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...
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