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The technique of completing the square was known in the Old Babylonian Empire. [5] Muhammad ibn Musa Al-Khwarizmi, a famous polymath who wrote the early algebraic treatise Al-Jabr, used the technique of completing the square to solve quadratic equations. [6]
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 of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...
Any generic method or algorithm for solving quadratic equations can be applied to an equation with symbolic coefficients and used to derive some closed-form expression equivalent to the quadratic formula. Alternative methods are sometimes simpler than completing the square, and may offer interesting insight into other areas of mathematics.
The process of completing the square makes use of the algebraic identity + + = (+), which represents a well-defined algorithm that can be used to solve any quadratic equation. [ 6 ] : 207 Starting with a quadratic equation in standard form, ax 2 + bx + c = 0
and they found square roots efficiently using division and averaging. [16] Problems of this type included finding the dimensions of a rectangle given its area and the amount by which the length exceeds the width. Tables of values of n 3 + n 2 were used to solve certain cubic equations. For example, consider the equation:
This use of variables entails use of algebraic notation and an understanding of the general rules of the operations introduced in arithmetic: addition, subtraction, multiplication, division, etc. Unlike abstract algebra , elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers .
The Philippines began looking into completing Bataan. Part of the Fukushima Daiichi nuclear plant that flooded on March 11, 2011 in Fukushima Prefecture, Japan, triggering the worst nuclear ...
Completing the square; Conjugate (square roots) ... Solving quadratic equations with continued fractions; T. ... By using this site, ...