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
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