>> Use the quadratic formula to
solve t squared equals t plus 8.
Again we're going to want to get
all of the terms on the same side
of the equation so that the other side equals 0.
In this case it might be tempting to
subtract t squared from both sides
to move that t squared to the right.
But then we would have a negative t
squared and we generally don't want
to have a negative leading coefficient.
It is allowed, but it's something that makes the
calculations just a little bit more complicated.
And in general it's not something that
I like to devote time to in class.
So we're going to make sure when we're
deciding which side to get all of our terms on,
to make sure that the leading coefficient
is positive just to make things easier.
In this case that means we want to move
all the terms to the left hand side.
If we subtract t on both sides, and
then also subtract 8 on both sides.
On the left that's going to leave us
with t squared minus t and minus 8.
And then on the right hand side
everything cancels and we're left with 0.
Now at this point we're ready
to use the quadratic formula.
The value of a is 1, the value of b is
negative 1, the value of c is negative 8.
And we can start plugging things
in to the quadratic formula.
We start with the opposite of b. Since b is
negative 1, the opposite of b is positive 1.
Then we have plus or minus the square root
of b squared, in this case b squared is 1.
Then minus 4 times a, which is
1 times c which is negative 8.
All over 2 times a, which
is going to be 2 times 1.
Now underneath that radical
we can do some evaluating.
That subtraction is going
to turn into an addition,
because the 2 negatives will
cancel each other out.
And then 4 times 1 times 8 is 32.
Then in the denominator 2 times 1 is 2.
And when we add the 1 and the 32 underneath the
radical, we end up with the square root of 33.
That's all over 2.
If we split this up into 2 fractions, we have
1/2 plus or minus the square root of 33 over 2.
And in this case there's
no simplifying we can do.
The fractions don't reduce, the radical can't
be simplified, we can't combine any like terms.
And so this is just going to be
our final answer, x equals 1/2 plus
or minus the square root of 33 over 2.
