>> Use the quadratic formula to
solve 18y squared minus 7y equals 1.
Before we use the quadratic formula, we
need to get this in standard form and what
that means is getting the constant term on
the left because the quadratic formula works
for any quadratic equation in the form
ax squared plus bx plus c equals 0.
We need all of the terms on one
side and then the other side equal
to 0 before we can apply the quadratic formula.
So, to move that 1 to the left, we're
going to subtract 1 on both sides
and that gives us 18y squared
minus 7y minus 1 equals 0.
And, now we're able to use
the quadratic formula.
In this case, a equals 18, b equals
negative 7, and c equals negative 1.
Let's try to use the quadratic formula
without writing it down this time.
In this case, we start off with the
opposite of b, but since b is negative 7,
the opposite of b is positive
7, so we start off with 7,
plus or minus the square root of b squared.
In this case, b is negative 7.
Negative 7 squared is 49 and then minus 4 times
a, which is 18, times c, which is negative 1,
and this is all over 2 times a,
which is going to be 2 times 18.
Now, let's look underneath that radical.
We've got 7 plus or minus the square root
of 49 and this is going to become a plus,
these two negatives will cancel each other
out, 4 times 18 is 72 and times 1 is still 72.
So, we've got 49 plus 72 under the radical.
And, in the denominator, 2 times 18 is 36.
Now, underneath that radical, 49 plus 72 is 121.
So, we've got 7 plus or minus
the square root of 121 over 36.
And, the square root of 121 is 11.
So, we end up with x equals
7 plus or minus 11 over 36.
And, what we're going to do is we're going
to look at those two solutions separately,
x equals 7 plus 11 over 36 or
x equals 7 minus 11 over 36.
We're separating them out
so we can do the arithmetic
and simplify each of them on their own.
Now, for the first one, 7 plus 11 is 18,
so we've got 18/36, which reduces to 1/2.
And, then in the second solution,
7 minus 11 is negative 4
and negative 4/36 reduces to negative 1/9.
So, in this case, we end up with x equals 1/2
or x equals negative 1/9 and
this is our final answer.
