Welcome to a tutorial on
how to solve equations
on the TI-89 graphing calculator.
To begin, I do have the
calculator set to exact mode.
If we press the mode key,
and then F2 for page 2
notice how down here it does say exact.
If we arrow down to see exact
and press the right arrow, remember
there are three options,
automatic, exact and approximate.
I prefer the exact mode.
In exact mode if we want
the approximate value
we can always press diamond enter.
So I'm going to go ahead and press Enter.
Then Enter.
Whenever solving an equation
that has a real solution
we can use the solve function under the
algebra menu which is F2.
So to solve the equation,
three x plus seven equals 19
we'll press F2, notice how
solve is the first option.
So you can press one or enter.
I'm going to press enter.
Enter the equation, three
x plus seven equals 19.
We want to solve for the
variable x so we enter comma x
closed parentheses and Enter.
The solution is x equals four.
Next we want to solve x squared minus
two x minus 15 equals zero.
So F2 enter.
Enter the equation, x
raised to the power of two
minus two x, notice how
I accidentally pressed z.
So to clear this, I just
press the back arrow,
enter the x and continue.
So, minus 15 equals zero.
We're solving for x so comma x,
Closed Parentheses, and enter.
Notice how we have two
solutions, x equals five
or x equals negative three.
Our next equation is
another quadratic equation
but this one's not factorable,
so enter F2, enter,
two x raised to the
power of two plus four x
minus five equals zero comma
x closed parentheses, enter.
Notice we have two real
irrational solutions
which means you would have had to solve
this using the quadratic formula.
It is important to be
aware that sometimes the 89
will show the solution in a different form
than we're used to seeing.
Notice how when we apply
the quadratic formula
we normally don't have
parentheses in the solution.
But these two solutions
would be equivalent
to the solutions we would find
using the quadratic formula.
Next, we have an exponential equation.
So we'll press F2 enter.
And we have e raised to the power of two x
so enter diamond x which brings up
e raised to the power of two x
closed parenthesis plus five equals 12.
Again, we're solving for x.
So we enter comma x, closed
parenthesis and enter.
And notice our exact solution is x equals
natural log seven divided by two.
And again, keep in mind
if we have a solution
that involves a natural log, it can
be written in different forms
or with logs of different bases.
Because our solution contains natural log
we'd have to solve this equation by hand
using natural log in order to get
the solution in this form.
And then finally for our last equation,
we have x squared plus four equals zero.
So let's press F2 and
then option one for solve
and then enter for the first option solve
and we'll enter x raised to
the power of two plus four
equals zero comma x closed
parenthesis and enter.
And notice how the
calculator is saying false,
which is telling us this equation
does not have any real solutions.
The solutions are going to be complex.
So we'll have to use
cSolve rather than solve
in order to solve this last equation.
So let's go ahead a press F2,
arrow down to complex, right arrow once
and we want to select cSolve
which is the first option.
So you can press one or enter.
Now enter the equation again.
So we have x raised to the power of two
plus four equals zero comma x
closed parenthesis and enter.
Notice how we have two
complex or imaginary solutions
x equals two i or x equals negative two i.
I hope you found this helpful.
