We have a problem here that we're gonna
solve using the quadratic formula but I
hope you notice that it's not exactly
like any quadratic formula problem we've
worked so far. Because the exponent
is higher than a 2, for starters. So let's
go ahead and subtract the 2.9. We know we
need to get everything on one side and 0
on the other. Now the next step is
recognizing that when I go to
factor this... if I could factor it... 
I can't factor it. But if I tried
I would have (x^2 +    )(x^2 +   ), right?
There'd also be some numbers here in the
front if I could factor it. But when
I get down to the end I'm gonna have x^2
and some constant = 0, right?
I'm gonna be solving for x^2 here
and not x. So you know when we write the
quadratic formula, we always write x
equals -b +/- ... 
and it's because we're finding a
single value of x. And what I'm saying
i'm going to do different here is that
I'm going to be solving for an x^2,
right? So that's always true if the
powers go up to 6 or 8... 
it would be x^3, if it was x^6 or
something like that. We wouldn't go that
high but anyway... that's the gist of
this problem is that you do apply a
quadratic formula but you just apply it
and you get x^2's at the end. So
let's apply the quadratic formula here.
So I'm gonna do again x^2 equals...
negative... and then b is -1.5
plus or minus the square root
of (-1.5)^2 - 4*(3.8)*(-2.9).
And we're gonna divide all of that
by 2*(3.8), right? So let's work through
these numbers here. Double negative of
1.5 is +1.5 plus or minus the
square root of 2.25... and now here I have
two negatives... -4 and this
-2.9. That's two
negatives become positive.
And now the product of
these three numbers is 44.08
And then I divide all of that by 7.6
Alright let's find out what 
2.25 + 44.08 is...
1.5 plus or minus the square root of...
that's 46.33... and
we're gonna divide that by 7.6
Alright so now I have square root
of 46.33. Let me
go ahead and find the square root of
that number. And it's 6.8066
Let me just grab that many
decimals. So this is 6.8066
So my two solutions here are
going to be:
x^2 = (1.5 + 6.8066)/7.6
And I have (1.5 - 6.8066)/7.6
So let's go ahead do this first one here.
1.5 + 6.8066 is 8.3066.
And we're gonna divide by 7.6
So I get 1.09297.
Alright now on this side, I
have 1.5 - 6.8066
and I'm gonna divide that by
7.6. And so there I get
-0.6982.
Now keep in mind, these are x^2
values. So if we want to find x
for those two values... 
let's go over here and break it up...
we have x^2 = 1.09297.
We take the
square root of both sides.
Remember when we do 
square root method, we need to do +/-
whatever this result is so
1.09297... and
take the square root
And I get 1.045. Alright it wants three
decimals for the final answer.
So +/- 1.045. That's
two of my solutions...
a +1.045 and a -1.045.
Now on the other side I
have x^2 equals a negative number.
Alright so for this question, if we
take square root of both sides, we're
going to be in trouble because these are
imaginary. So in this case, we're
going to discard these imaginary numbers.
They are not part of the solution for
this. I understand there may be some
confusion because when we do quadratic
formula with a regular x^2, we
do process imaginary numbers as
potential solutions but here since this
is x^4 and we're solving for
x^2, it's not possible for that to
be true. So our two solutions here will be
1.045
and -1.045. And those are the
two solutions you would enter here in
the box.
