generate steps for completing the square of a quadratic expression
CompleteSquareSteps( expr, variable )
CompleteSquareSteps( expr, implicitmultiply = true )
string or expression
(optional) variable to collect the terms by
output = ...
(optional) option to control the return value
displaystyle = ...
(optional) option to control the layout of the steps
The CompleteSquareSteps command accepts a polynomial and displays the steps required to complete the square. As a pre-step, the given expression will be reorganized into the general form of a quadratic by expanding and simplifying as needed.
An optional variable can be provided as a second argument. This so called variable can also be an expression, such as sin(t) for completing the square to the form (sin(t)+a)^2+b. If no variable is provided, the return of indets(expression,name) will be used to find the first variable that has has degree 2.
If expr is a string, then it is parsed into an expression using InertForm:-Parse so that no automatic simplifications are applied, and thus no steps are missed.
The implicitmultiply option is only relevant when expr is a string. This option is passed directly on to the InertForm:-Parse command and will cause things like 2x to be interpreted as 2*x, but also, xyz to be interpreted as x*y*z.
The output and displaystyle options are described in Student:-Basics:-OutputStepsRecord. The return value is controlled by the output option.
This function is part of the Student:-Basics package.
=•Bring terms to left-sidex+1⁢x−3−4⁢x−2=0•Collect in terms ofxx2−6⁢x−5=0•Add and subtract−622=0•Simplify terms=0•The first3terms can be regrouped as a perfect square=0•Simplify the remaining term=0
The Student:-Basics:-CompleteSquareSteps command was introduced in Maple 2023.
For more information on Maple 2023 changes, see Updates in Maple 2023.
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