Answer:


Step-by-step explanation:
Let's expand both sides.
I'm going to use the following identity to expand the binomial squared expressions:
or
.
Left-hand side:



Reorder so
's are together and that ![x[tex]'s are together.[tex](x^2+4x^2)+(-2ax-4bx)+(a^2+b^2)](https://tex.z-dn.net/?f=x%5Btex%5D%27s%20are%20together.%3C%2Fp%3E%3Cp%3E%5Btex%5D%28x%5E2%2B4x%5E2%29%2B%28-2ax-4bx%29%2B%28a%5E2%2Bb%5E2%29)

Right-hand side:



Reorder so
's are together and that ![x[tex]'s are together.[tex](x^2+4x^2)+(-6x)+9](https://tex.z-dn.net/?f=x%5Btex%5D%27s%20are%20together.%3C%2Fp%3E%3Cp%3E%5Btex%5D%28x%5E2%2B4x%5E2%29%2B%28-6x%29%2B9)

Now let's compare both sides.
If we want both sides to appear exactly the same we need to choose values
and
such the following are true equations:


So if we solve the system we can find the values
and
such that the left=right.
Let's solve the first equation for
in terms of
.
Add
on both sides:

Divide both sides by -4:

Reduce (divide top and bottom by -2):

Now let's plug this into second equation:


(I used the identity
)
Multiply both sides by 4 to clear the fractions from the problem:

Combine like terms on left hand side:


Subtract 36 on both sides:

Now let's try to factor.
We are going to try to find two numbers that multiply to be 5(-27) and add to be -6.
5(-27)=(5*3)(-9)=15(-9)=-15(9) while -15+9=-6.
So let's replace
with
and factor by grouping.



This implies
or
.
Solving the first is easy. Just ad 3 on both sides to get:
.
The second requires two steps. Subtract 9 and then divide by 5 on both sides.

.
So let's go back to finding
now that we know the
values.
If
and
,
then
.
So one ordered pair
that satisfies the equation is:
.
If
and
,
then
.
Let's multiply top and bottom by 5 to clear the mini-fraction.



So one ordered pair
that satisfies the equation is:
.