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Completing the square can be used to derive a general formula for solving quadratic equations, called the quadratic formula. [9] The mathematical proof will now be briefly summarized. [ 10 ] It can easily be seen, by polynomial expansion , that the following equation is equivalent to the quadratic equation: ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 ...
In elementary algebra, the quadratic formula of math solving basic integral outputs 1 is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations, such as completing the square , yield the same solutions.
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 ...
Completing the square is the oldest method of solving general quadratic equations, used in Old Babylonian clay tablets dating from 1800–1600 BCE, and is still taught in elementary algebra courses today.
Toggle Solving a quartic equation, special cases subsection ... which is a simple quadratic equation, whose solutions are easily found using the quadratic formula ...
Each coordinate of the intersection points of two conic sections is a solution of a quartic equation. The same is true for the intersection of a line and a torus.It follows that quartic equations often arise in computational geometry and all related fields such as computer graphics, computer-aided design, computer-aided manufacturing and optics.
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.
An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.