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:
“It is almost as if you were frantically constructing another world while the world that you live in dissolves beneath your feet, and that your survival depends on completing this construction at least one second before the old habitation collapses.”
—Tennessee Williams (1914–1983)
“This house was designed and constructed with the freedom of stroke of a forester’s axe, without other compass and square than Nature uses.”
—Henry David Thoreau (1817–1862)