I want to solve this equation using the quadratic
formula.
So, notice, I'm not in the right form.
I've got to have it equal to zero so I can
figure out what a, b, and c are.
So the first things I'm going to do here are
just move everything to one side so that it's
equal to zero.
For my sanity, I'm just going to keep the
4 x squared over here so that it's positive.
You wouldn't have to, since the formula can
take positives or negatives just as easily,
but I find it easier just to have my coefficient
on x...or my a value positive because I'm
dividing by it times 2 in the end.
And then I don't need to worry about the sign
on the whole thing being messed up because
I screwed up somehow.
Now I've got it in this form, 4 x squared
plus 12 x plus 9 equals 0.
I can see that a is equal to 4.
This time b is equal to negative 12.
And c is equal to 9.
Okay?
So, I want to use those values and substitute
them into x equals negative b plus or minus
the square root of b squared minus 4 times
a times c, all divided by 2 a.
Alright, so let's get the values in here.
So x equals negative, negative 12, plus or
minus the square root of negative 12, squared
minus 4 times, a is 4, times c, which is 9,
all divided by 2 times a, oops, a, which is
4.
Okay.
Checking my pretty colors here, I see that
a was 4, a ended up in the two spots that
a should.
b is negative 12, it's in the right places,
with parentheses because it was negative,
to make sure I don't mess that up.
And then c was 9, it's in the one spot it
should be.
So let's start to simplify this expression.
So I've got x is the opposite of negative
12 is positive 12.
Plus or minus the square root, negative 12
times negative 12 should be positive, and
it's positive 144.
I only see the minus sign, there are no negatives,
so minus 4 times 4 is 16 times 9, we 16 times
9 is the same as 4 times 3 times 4 times 3
is 12 times 12 is 144.
All divided by 2 times 4, which is 8.
Okay, so x is 12 plus or minus the square
root of 144 minus 144 is 0, eighths.
The square root of 0 is 0.
So 12 plus or minus 0, all divided by 8.
So x is either 12 plus 0 over 8 or x is 12
minus 0 over 8.
Here I have x is 12 eighths, that simplifies
to...easy...3 halves.
Here I also have x is 12 eighths, which is
3 halves.
So 3 halves seems to be the only solution
to this equation because I got it for both
sides, which is fine.
So I think it's 3 halves or 1 point 5.
Let's do a quick check.
I forgot to copy it, so let's go up here.
Grab this guy.
Go to the next page.
Put this guy, and I want to check 3 halves.
So I want to know if 4 times 3 halves squared
is the same as 12 times 3 halves minus 9.
4 times three halves is 4 times 9 fourths
because 3 halves times 3 halves is...3 times
3 is 9, 2 times 2 is 4.
I want to know if that is, let's see, 12 times
3 halves, half of 12 is 6, times 3 is 18.
4 times 9 fourths is 9.
18 minus 9 is 9.
I've got it.
3 halves is definitely the solution to that
quadratic equation and it's the only one.
