How to Solve for x on the TI-89: solve and nSolve

You have an equation and you need x. The TI-89 Titanium has four commands for that, and picking the wrong one is why so many people search for how to solve for x on the TI-89. This guide shows which one to use, the exact keys, and what the result looks like, including when you need TI-89 nSolve.

The short version

solve( for an equation, exact answers, all solutions. Start here.
zeros( for an expression that should equal zero, answers as a list.
nSolve( when there is no exact answer and you want one decimal root.
cSolve( and cZeros( when the roots can be complex.

All of them are in the F2 Algebra menu on the HOME screen, and all of them need the variable as the last argument.

solve(: exact solutions of an equation

Press F2 and 1 (or ENTER on the first item) to paste solve( into the edit line. Type the equation with the = key, a comma, the variable, and close the parenthesis.

F21→ solve(

solve( examples
Input	Result
solve(x^2=9,x)	x=−3 or x=3
solve(x^2-2=0,x)	x=−√2 or x=√2

Two things to notice. The answer is written as an equation joined by or, so you can see every solution at once. And irrational roots stay exact: √(2), not a decimal. If you need the decimal, press ◆ ENTER instead of ENTER, as described in our guide on decimal answers.

solve( also works with letters. solve(a*x+b=c,x) treats a, b and c as constants and returns x as a formula, which is how you rearrange a physics formula for one quantity. Write a*x with the multiply sign; ax would be read as a single variable named ax.

zeros(: roots as a list

zeros( takes an expression instead of an equation and returns the values of x that make it zero. It is item 4 in F2. The result is a list in braces, which is useful when you want to keep working with the roots: store the list, or take one element with an index.

F24→ zeros(

zeros( example
Input	Result
zeros(x^2-9,x)	{−3,3}

Compare this row with the first solve( example. Same polynomial, same roots, different format. Use whichever fits the next step.

nSolve(: one decimal root, fast

Some equations have no closed form, for example when x appears both inside and outside a cosine or an exponential. solve( may then return the equation unchanged or take a long time. nSolve( skips the algebra and searches numerically for one root, returned as a decimal. It is item 8 in F2.

F28→ nSolve(

nSolve( example
Input	Result
nSolve(x^2=2,x)	1.41421356237

nSolve( returns one root even when there are several. To steer it toward the one you want, add a condition with the with operator on the handheld, for example nSolve(equation,x)|x>0 for the positive root. In Calc89 you can also pass a lower and an upper bound: nSolve(equation,x,low,high). Graphing the function first shows you roughly where each root is.

|→ | (with)

Complex roots: cSolve( and cZeros(

An equation like x² = −4 has no real solution, so solve( cannot give you a real x. To get the complex solutions, use the complex versions in the Complex submenu of F2.

F2►►1→ cSolve(

Complex solutions
Input	Result
cSolve(x^2=-4,x)	x=−2·ⅈ or x=2·ⅈ
cZeros(x^2+1,x)	{−ⅈ,ⅈ}

ⅈ is 2nd CATALOG. Our article on complex numbers on the TI-89 covers polar form and the other complex commands.

Polynomials: polyRoots(

Calc89 also has polyRoots( in the catalog. For a polynomial it returns the roots as a list, much like zeros(.

polyRoots( example
Input	Result
polyRoots(x^2-5x+6,x)	{2,3}

Why solve( does not work: common errors

x has a stored value. If you once stored 3 in x, solve(x^2=9,x) no longer sees an unknown. Delete it with DelVar x, or clear all one letter variables with NewProb (2nd F1, Clean Up).
The variable is missing. solve(x^2=9) without ,x gives an error. The variable always comes last.
Implied multiplication. 2x works, but xy and x(x+1) do not mean what you think. Type x*y and x*(x+1).
Wrong angle mode. Trig equations solved in DEGREE give answers in degrees; check MODE before you trust the numbers.
Expecting a decimal. An exact answer with roots or π is correct, not an error. Use ◆ ENTER for the decimal.

Two or more variables

solve( also handles systems. Join the equations with and and give the variables in braces, for example solve(x+y=5 and x-y=1,{x,y}). The result lists one value per variable. For larger linear systems the matrix method with rref( is often quicker; the linear algebra guide shows both.

In Calc89

Calc89 is intended for use with TI-89 Titanium, and the F2 Algebra menu is laid out the same way: solve(, factor(, expand(, zeros(, approx(, comDenom(, propFrac( and nSolve(, with the complex commands in their own submenu. Every example in the tables above was computed by the same CAS that runs in the app.

If the equation is on paper, point the camera scanner at it, printed or handwritten, and it lands in the edit line ready to solve. The AI keystroke tutor then shows which command fits and the key sequence for it, step by step, so you can repeat it on the handheld in class.

Frequently asked questions

Why does solve( not give the answer I expect?

Usually x has a stored value. Delete it with DelVar x or run NewProb from the Clean Up menu, then solve again.

What is the difference between solve( and nSolve(?

solve( works symbolically and returns every solution it finds, exact where possible. nSolve( searches numerically and returns one decimal solution.

Can the TI-89 solve for x in terms of other letters?

Yes. solve( treats every letter except the one you name as a constant, so the result is a formula.

How to Solve for x on the TI-89 Titanium: solve, zeros and nSolve