In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form
to the form
In this context, "constant" means not depending on x. The expression inside the parenthesis is of the form (x − constant). Thus one converts ax2 + bx + c to
and one must find h and k.
Completing the square is used in
- solving quadratic equations,
- graphing quadratic functions,
- evaluating integrals in calculus, such as Gaussian integrals with a linear term in the exponent
- finding Laplace transforms.
In mathematics, completing the square is considered a basic algebraic operation, and is often applied without remark in any computation involving quadratic polynomials.
Read more about Completing The Square: Relation To The Graph, Solving Quadratic Equations, Geometric Perspective, A Variation On The Technique
Famous quotes containing the words completing and/or square:
“The inhabitants of St. John’s and vicinity are described by an English traveler as “singularly unprepossessing,” and before completing his period he adds, “besides, they are generally very much disaffected to the British crown.” I suspect that that “besides” should have been a “because.””
—Henry David Thoreau (1817–1862)
“I would say it was the coffin of a midget
Or a square baby
Were there not such a din in it.”
—Sylvia Plath (1932–1963)