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Completing the square is used in. solving quadratic equations, deriving the quadratic formula, graphing quadratic functions, evaluating integrals in calculus, such as Gaussian integrals with a linear term in the exponent, [1] finding Laplace transforms. [2][3] In mathematics, completing the square is often applied in any computation involving ...
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 ...
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.)
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 ...
Gaussian integral. A graph of the function and the area between it and the -axis, (i.e. the entire real line) which is equal to . The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function over the entire real line. Named after the German mathematician Carl Friedrich Gauss, the integral is.
Ptolemy's theorem is a relation among these lengths in a cyclic quadrilateral. In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius ...
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.
A mathematical exercise is a routine application of algebra or other mathematics to a stated challenge. Mathematics teachers assign mathematical exercises to develop the skills of their students. Early exercises deal with addition, subtraction, multiplication, and division of integers. Extensive courses of exercises in school extend such ...