Completing the square

In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form

to the form

for some values of h and k.

In other words, completing the square places a perfect square trinomial inside of a quadratic expression.

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,
• finding Laplace transforms.

In mathematics, completing the square is often applied in any computation involving quadratic polynomials.