SOLUTION: I'm a little confused on how to work this one... 4x^4 - 12x^2 - 19 = 0 I use subtitution of y = x^2 giving me 4y^2 - 12y - 19 = 0 My answers are y = 4.145751311 and -1.

Question 353963: I'm a little confused on how to work this one...
4x^4 - 12x^2 - 19 = 0
I use subtitution of y = x^2 giving me
4y^2 - 12y - 19 = 0
My answers are y = 4.145751311 and -1.145751311
Now I'm not sure what to do from here.
Thanks a lot for your help!
Neil
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's solve

Start with the given equation.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "y":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

So the solutions in terms of y are or

But remember that . So

or

Do you think you can take it from here?

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

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