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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 x − h {\displaystyle x-h} , this expression is a quadratic polynomial with no linear term.
He presented a method of completing the square to solve quadratic equations, sometimes called Śrīdhara's method or the Hindu method. Because the quadratic formula can be derived by completing the square for a generic quadratic equation with symbolic coefficients, it is called Śrīdharācārya's formula in some places.
This method for completing the square is ancient and was known to the 8th–9th century Indian mathematician Śrīdhara. [12] Compared with the modern standard method for completing the square, this alternate method avoids fractions until the last step and hence does not require a rearrangement after step 3 to obtain a common denominator in the ...
For example, for the family of quadratic functions having the general form = + +, the simplest function is =, and every quadratic may be converted to that form by translations and dilations, which may be seen by completing the square. This is therefore the parent function of the family of quadratic equations.
In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as [1] + + =, where the variable x represents an unknown number, and a, b, and c represent known numbers, where a ≠ 0.
By definition, equality is an equivalence relation, meaning it is reflexive (i.e. =), symmetric (i.e. if = then =), and transitive (i.e. if = and = then =). [33] It also satisfies the important property that if two symbols are used for equal things, then one symbol can be substituted for the other in any true statement about the first and the ...
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Babylonian mathematics is a range of numeric and more advanced mathematical practices in the ancient Near East, written in cuneiform script.Study has historically focused on the First Babylonian dynasty old Babylonian period in the early second millennium BC due to the wealth of data available.