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Animation depicting the process of completing the square. (Details, animated GIF version) In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of and . [1] In terms of a new quantity , this expression is a quadratic ...
To complete the square, form a squared binomial on the left-hand side of a quadratic equation, from which the solution can be found by taking the square root of both sides. The standard way to derive the quadratic formula is to apply the method of completing the square to the generic quadratic equation a x 2 + b x + c = 0 {\displaystyle ...
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.)
One can consider a Latin square as a complete bipartite graph in which the rows are vertices of one part, the columns are vertices of the other part, each cell is an edge (between its row and its column), and the symbols are colors. The rules of the Latin squares imply that this is a proper edge coloring.
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
Square (algebra) 5⋅5, or 52 (5 squared), can be shown graphically using a square. Each block represents one unit, 1⋅1, and the entire square represents 5⋅5, or the area of the square. In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation.
Parabola. Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward. The parabola is a member of the family of conic sections. In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U ...
A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order n over two sets S and T (which may be the same), each consisting of n symbols, is an n × n arrangement of cells, each cell containing an ordered pair (s, t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells ...