SOLUTION: Can you please help me solve this problem?!!? {{{9x^4=25x^2-16}}} The directions say: solve the equation by making the appropriate substitution. Here is what I have so far....b

Question 180326: Can you please help me solve this problem?!!?
The directions say: solve the equation by making the appropriate substitution.
Here is what I have so far....but I am stuck.

At this point I wasn't sure. Do I use the quadratic formula??? I tried that but just got confused. Please help. Thanks.
Found 3 solutions by Alan3354, jim_thompson5910, stanbon:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!

----------------
Sub u for x^2
You used 3u for one term, and u for the other.
You can factor"
(9u-16)*(u-1) = 0
u = 1, u = 16/9
Then
x = +1, -1
x = +4/3, -4/3
--------------
Another approach is to "eyeball" the 9, -25, 16 and spot that +1 and -1 are solutions, factor those out, then you have a quadratic.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Let . This means that

Replace with and with

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for u

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

---------------------------------------

Now remember, we let , so this means that

or

Let's solve the first equation :

Take the square root of both sides

or Break up the "plus/minus"

or Take the square root of to get

So the first two solutions are or

------------------------------

Now let's solve the second equation :

Take the square root of both sides

or Break up the "plus/minus"

or Take the square root of to get

So the next two solutions are or

======================================================

Answer:

So the 4 solutions are:

, , or
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
9x^4=25x^2-16
9x^4 - 25x^2 + 16 = 0
Quadratic Formula:
x^2 = [25 +- sqrt(625 - 4*9*+16)]/18
x^2 = [25 +- sqrt(49)]/18
x^2 = [25 + 7]/18 or x^2 = [25 - 7]/18
x^2 = 16/9 or x^2 = 1
x = (4/3) or x = (-4/3) or x = 1 or x= -1
===============================================
Cheers
Stan H.
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