SolveSteps - Maple Help

Student[Basics]

 SolveSteps
 show steps in the solution of a specified problem

 Calling Sequence Student[Basics][SolveSteps](ex, variable, opts)

Parameters

 ex - expression or equation variable - (optional) variable to solve for opts - options of the form keyword=value where keyword is one of displaystyle, output

Description

 • The SolveSteps command is used to show the steps of solving a basic student problem.
 • If ex is an equation the variable in equation is solved for. If ex is given as an expression, the expression is solved for assuming ex=0.
 • If only one variable exists in ex, it is not necessary to specify a variable to solve for. If there are two or more variables in ex, a variable to solve for must be given for variable.
 • The displaystyle and output options can be used to change the output format.  See OutputStepsRecord for details.

Package Usage

 • This function is part of the Student[Basics] package, so it can be used in the short form SolveSteps(..) only after executing the command with(Student[Basics]). However, it can always be accessed through the long form of the command by using Student[Basics][SolveSteps](..).

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Basics}\right]\right):$
 > $\mathrm{SolveSteps}\left(5\mathrm{exp}\left(4x\right)=16\right)$
 $\begin{array}{lll}{}& {}& \text{Let's solve}\\ {}& {}& \left[{}\right]{=}{16}\\ \text{▫}& {}& \text{Convert from exponential equation}\\ {}& \text{◦}& {\text{Divide both sides by}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{5}\\ {}& {}& \left[{}\right]{=}\left[{}\right]\\ {}& \text{◦}& \text{Simplify}\\ {}& {}& \left[{}\right]{=}\frac{{16}}{{5}}\\ {}& \text{◦}& \text{Apply ln to each side}\\ {}& {}& \left[{}\right]{=}\left[{}\right]\\ {}& \text{◦}& \text{Apply ln rule: ln(e^b) = b}\\ {}& {}& {4}{}{x}{=}{\mathrm{ln}}{}\left(\frac{{16}}{{5}}\right)\\ \text{•}& {}& {\text{Divide both sides by}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{4}\\ {}& {}& \left[{}\right]{=}\left[{}\right]\\ \text{•}& {}& \text{Exact solution}\\ {}& {}& {x}{=}\frac{{\mathrm{ln}}{}\left(\frac{{16}}{{5}}\right)}{{4}}\\ \text{•}& {}& \text{Approximate solution}\\ {}& {}& {x}{=}{0.2907877025}\end{array}$ (1)
 > $\mathrm{SolveSteps}\left({x}^{2}-b,x\right)$
 $\begin{array}{lll}{}& {}& \text{Let's solve}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Set expression equal to 0}\\ {}& {}& \left[{}\right]{=}{0}\\ \text{•}& {}& {\text{Add}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{b}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{to both sides}}\\ {}& {}& \left[{}\right]{=}\left[{}\right]\\ \text{•}& {}& \text{Simplify}\\ {}& {}& \left[{}\right]{=}{b}\\ \text{•}& {}& \text{Take Square root of both sides}\\ {}& {}& {x}{=}{±}\left[{}\right]\\ \text{•}& {}& \text{Solution}\\ {}& {}& {x}{=}\left(\sqrt{{b}}{,}{-}\sqrt{{b}}\right)\end{array}$ (2)
 > $\mathrm{SolveSteps}\left({x}^{3}+4{x}^{2}+4x,\mathrm{output}=\mathrm{typeset}\right)$
 $\begin{array}{lll}{}& {}& \text{Let's solve}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Set expression equal to 0}\\ {}& {}& \left[{}\right]{=}{0}\\ \text{•}& {}& \text{Factor}\\ {}& {}& {{x}}^{{3}}{+}{4}{}{{x}}^{{2}}{+}{4}{}{x}{=}{0}\\ \text{•}& {}& {\text{Common factor}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Examine term:}\\ {}& {}& {{x}}^{{2}}{+}{4}{}{x}{+}{4}{=}{0}\\ \text{▫}& {}& \text{Apply the AC Method}\\ {}& \text{◦}& \text{Examine quadratic}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& {\text{Look at the coefficients,}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{A}{}{{x}}^{{2}}{+}{B}{}{x}{+}{C}\\ {}& {}& \left[{"A"}{=}{1}{,}{"B"}{=}{4}{,}{"C"}{=}{4}\right]\\ {}& \text{◦}& {\text{Find factors of |AC| = |}}\left[{}\right]{\text{| =}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{4}\\ {}& {}& \left\{{1}{,}{2}{,}{4}\right\}\\ {}& \text{◦}& {\text{Find pairs of the above factors, which, when multiplied equal}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{4}\\ {}& {}& \left\{\left[{}\right]{,}\left[{}\right]\right\}\\ {}& \text{◦}& {\text{Which pairs of these factors have a}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{sum}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{of B =}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{4}{\text{? Found:}}\\ {}& {}& \left[{}\right]{=}{4}\\ {}& \text{◦}& \text{Split the middle term to use above pair}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& {\text{Factor}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{out of the first pair}}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& {\text{Factor}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{2}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{out of the second pair}}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& {x}{+}{2}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{is a common factor}}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& \text{Group common factor}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{This gives:}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& {\text{The}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{1st}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{factor is}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{which implies}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{= 0 is a solution}}\\ {}& {}& {x}{=}{0}\\ \text{•}& {}& {\text{Set}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{2nd}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{factor}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}{+}{2}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{to 0 to solve}}\\ {}& {}& {x}{+}{2}{=}{0}\\ \text{▫}& {}& {\text{Solution of}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}{+}{2}{=}{0}\\ {}& \text{◦}& {\text{Subtract}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{2}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{from both sides}}\\ {}& {}& \left[{}\right]{=}\left[{}\right]\\ {}& \text{◦}& \text{Simplify}\\ {}& {}& {x}{=}{-2}\\ \text{•}& {}& \text{Solution}\\ {}& {}& {x}{=}\left({-2}{,}{0}\right)\end{array}$ (3)
 > $\mathrm{SolveSteps}\left({x}^{3}+4{x}^{2}+4x,\mathrm{mode}=\mathrm{Learn}\right)$
 $\begin{array}{lll}{}& {}& \text{Let's solve}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Set expression equal to 0}\\ {}& {}& \left[{}\right]{=}{0}\\ \text{•}& {}& \text{Factor}\\ {}& {}& {{x}}^{{3}}{+}{4}{}{{x}}^{{2}}{+}{4}{}{x}{=}{0}\\ \text{•}& {}& {\text{Common factor}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{Examine term:}\\ {}& {}& {{x}}^{{2}}{+}{4}{}{x}{+}{4}{=}{0}\\ \text{▫}& {}& \text{Apply the AC Method}\\ {}& \text{◦}& \text{Examine quadratic}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& {\text{Look at the coefficients,}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{A}{}{{x}}^{{2}}{+}{B}{}{x}{+}{C}\\ {}& {}& \left[{"A"}{=}{1}{,}{"B"}{=}{4}{,}{"C"}{=}{4}\right]\\ {}& \text{◦}& {\text{Find factors of |AC| = |}}\left[{}\right]{\text{| =}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{4}\\ {}& {}& \left\{{1}{,}{2}{,}{4}\right\}\\ {}& \text{◦}& {\text{Find pairs of the above factors, which, when multiplied equal}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{4}\\ {}& {}& \left\{\left[{}\right]{,}\left[{}\right]\right\}\\ {}& \text{◦}& {\text{Which pairs of these factors have a}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{sum}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{of B =}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{4}{\text{? Found:}}\\ {}& {}& \left[{}\right]{=}{4}\\ {}& \text{◦}& \text{Split the middle term to use above pair}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& {\text{Factor}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{out of the first pair}}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& {\text{Factor}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{2}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{out of the second pair}}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& {x}{+}{2}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{is a common factor}}\\ {}& {}& \left[{}\right]\\ {}& \text{◦}& \text{Group common factor}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& \text{This gives:}\\ {}& {}& \left[{}\right]\\ \text{•}& {}& {\text{The}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{1st}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{factor is}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{which implies}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{= 0 is a solution}}\\ {}& {}& {x}{=}{0}\\ \text{•}& {}& {\text{Set}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{2nd}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{factor}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}{+}{2}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{to 0 to solve}}\\ {}& {}& {x}{+}{2}{=}{0}\\ \text{▫}& {}& {\text{Solution of}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{x}{+}{2}{=}{0}\\ {}& \text{◦}& {\text{Subtract}}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{2}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}{\text{from both sides}}\\ {}& {}& \left[{}\right]{=}\left[{}\right]\\ {}& \text{◦}& \text{Simplify}\\ {}& {}& {x}{=}{-2}\\ \text{•}& {}& \text{Solution}\\ {}& {}& {x}{=}\left({-2}{,}{0}\right)\end{array}$ (4)
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Compatibility

 • The Student[Basics][SolveSteps] command was introduced in Maple 2021.