Completing the Square

Completing the square is a technique in elementary algebra for converting a quadratic polynomial of the form ax^2 + bx + c into the form a(x - h)^2 + k, so that a quadratic problem is reduced to a simpler linear one once the squared term is isolated and a square root is taken. The name comes from a geometric picture in which x represents an unknown length, x^2 is the area of a square, and the term completes a larger square once a small square of side length b divided by 2a is added. It is the oldest known method for solving general quadratic equations, documented on Old Babylonian clay tablets from 1800 to 1600 BCE and later formalized by the mathematician Al-Khwarizmi in his treatise Al-Jabr. The method remains central to elementary algebra, to graphing quadratic functions, to deriving the quadratic formula, and to calculus techniques such as evaluating Gaussian integrals and finding Laplace transforms. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/