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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 h and k. In other words, completing the square places a perfect square trinomial inside of a quadratic expression.
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Hypercomplex number. In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex numbers in the late 19th century forms the basis of modern group representation theory.
Solving quadratic equations with continued fractions. In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is. where a ≠ 0. The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots ...
Completing_the_square.ogv (Ogg Theora video file, length 1 min 9 s, 640 × 480 pixels, 758 kbps, file size: 6.22 MB) This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. Description. Completing the square.ogv. Completing the ...
The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of can be found using difference of two squares: (since ) Therefore, the linear factors are and . Since the two factors found by this method are complex conjugates, we can use this in ...
Babylonian mathematics (also known as Assyro-Babylonian mathematics) [1][2][3][4] is the mathematics developed or practiced by the people of Mesopotamia, as attested by sources mainly surviving from the Old Babylonian period (1830–1531 BC) to the Seleucid from the last three or four centuries BC. With respect to content, there is scarcely any ...
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.