transform quadratic expressions to completed square form
CompleteSquare(f, x, ...)
algebraic expression, equation, or an inequality involving algebraic terms
(optional) name, function, list, or set
(optional) name or function
The CompleteSquare(f, x) command, where f is a quadratic expression, equation, or an inequality in x, completes the square of f. If f is not itself quadratic in x, its subexpressions are examined, and any which are quadratic in x are transformed to completed square form.
If x is a list or set, the operation of completing the square is applied successively to each component of x. These components can be names, such as u and v, or functions, such as sin⁡t and ⅆⅆwh⁡w.
The CompleteSquare(f) command is equivalent to CompleteSquare(f, indets(f,name)).
The command CompleteSquare(f, [x, y]) is equivalent to the command CompleteSquare(f, x, y).
The completed square form of the general quadratic expression a⁢x2+b⁢x+c is a⁢x+b2⁢a2+c−b24⁢a.
For a step-by-step solution that completes the square, see CompleteSquareSteps.
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