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.

Algebra ->  Quadratic Equations and Parabolas -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's solve 4y%5E2+-+12y+-+19+=+0+


4y%5E2-12y-19=0 Start with the given equation.


Notice that the quadratic 4y%5E2-12y-19 is in the form of Ay%5E2%2BBy%2BC where A=4, B=-12, and C=-19


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


y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


y+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%284%29%28-19%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-12, and C=-19


y+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%284%29%28-19%29+%29%29%2F%282%284%29%29 Negate -12 to get 12.


y+=+%2812+%2B-+sqrt%28+144-4%284%29%28-19%29+%29%29%2F%282%284%29%29 Square -12 to get 144.


y+=+%2812+%2B-+sqrt%28+144--304+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-19%29 to get -304


y+=+%2812+%2B-+sqrt%28+144%2B304+%29%29%2F%282%284%29%29 Rewrite sqrt%28144--304%29 as sqrt%28144%2B304%29


y+=+%2812+%2B-+sqrt%28+448+%29%29%2F%282%284%29%29 Add 144 to 304 to get 448


y+=+%2812+%2B-+sqrt%28+448+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


y+=+%2812+%2B-+8%2Asqrt%287%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


y+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29 or y+=+%2812-8%2Asqrt%287%29%29%2F%288%29 Break up the expression.


So the solutions in terms of y are y+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29 or y+=+%2812-8%2Asqrt%287%29%29%2F%288%29


But remember that y=x%5E2. So


x%5E2+=+%2812%2B8%2Asqrt%287%29%29%2F%288%29 or x%5E2+=+%2812-8%2Asqrt%287%29%29%2F%288%29


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