>> Use the quadratic formula to solve
8x squared plus x minus 9 equals 0.
In this case a equals 8, b equals 1, even
though the coefficient isn't written in,
we know that there's a 1 on
1x, and c equals negative 9.
And once we've identified the
values of the coefficient,
we can substitute everything
in to the quadratic formula.
We have x equals the opposite of b, in this case
that's negative 1, plus or minus the square root
of b squared, well 1 squared is 1,
minus 4 times a, which is 8, times c,
which is negative 9 all over
2 times a, which is 8.
So we've substituted everything in, now we
need to see what happens under the radical.
We have negative 1 plus or minus the square root
of 1, and that subtraction is going to change
into an addition, cause we've
got 2 negatives that cancel.
And then 4 times 8 times 9 is 288,
which is best done with a calculator.
And that's all over 2 times 8 which is 16.
Now we want to add 1 plus 288 is 289.
So we're going to have 289 in that radical.
And the square root of 289 is 17.
How did I know that?
I own a calculator.
Please use your calculators
with calculations like these.
If you do things by hand you are
much more likely to make mistakes.
So we have x equals negative 1
plus or minus 17 all over 16.
And this is where we're going to split up
the 2 solutions and look at them separately
so that we can simplify each on its own.
So we're going to have negative
1 plus 17 over 16.
Or x can be negative 1 minus 17 over 16.
Let's look at the first one.
Negative 1 plus 17 is 16, so
we have 16/16, which is just 1.
For the other solution negative
1 minus 17 is negative 18.
And negative 18 /16 reduces by 2.
When we reduce by 2 that
gives us negative 9 over 8.
And so we have our 2 solutions.
X equals 1 or x equals negative
9/8 and that's our final answer.
