SOLUTION: 2[(x)/(x+2)]^2 - 3[(x)/(x+2)] - 9 = 0 Can you help me?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 2[(x)/(x+2)]^2 - 3[(x)/(x+2)] - 9 = 0 Can you help me?      Log On


   

Question 992750: 2[(x)/(x+2)]^2 - 3[(x)/(x+2)] - 9 = 0
Can you help me?
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
2%28x%2F%28x%2B2%29%29%5E2-%283x%29%2F%28x%2B2%29-9+=+0

2%28x%5E2%2F%28x%2B2%29%5E2%29-3x%2F%28x%2B2%29-9=0

%282x%5E2%29%2F%28x%2B2%29%5E2-3x%2F%28x%2B2%29-9=0

Multiply through by (x+2)²

2x%5E2-3x%28x%2B2%29-9%28x%2B2%29%5E2=0

2x%5E2-3x%5E2-6x-9%28x%2B2%29%28x%2B2%29=0

-x%5E2-6x-9%28x%5E2%2B2x%2B2x%2B4%29=0

-x%5E2-6x-9%28x%5E2%2B4x%2B4%29=0

-x%5E2-6x-9x%5E2-36x-36=0

-10x%5E2-42x-36=0

Divide through -2}}}

5x%5E2%2B21x%2B18=0

%285x%2B6%29%28x%2B3%29=0

5x+6=0;   x+3=0
  5x=-6     x=-3
   x=-6/5

Edwin

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Or you can use u-substitution:

2%28x%2F%28x%2B2%29%29%5E2+-+3%28%28x%29%2F%28x%2B2%29%29+-+9+=+0

Let u=x%2F%28x%2B2%29

then the above becomes:

2u%5E2+-+3u+-+9+=+0

%28u-3%29%282u%2B3%29=0

u-3=0;  2u%2B3=0

u=3;  2u=-3

             u=-3%2F2

Then since  u=x%2F%28x%2B2%29

x%2F%28x%2B2%29=3;   x%2F%28x%2B2%29=-3%2F2

Mutiply both sides by x+2

x=3%28x%2B2%29;   2x=-3%28x%2B2%29

x=3x%2B6;      2x=-3x-6

-2x=6;        5x=-6

x=-3;          x=-6%2F5

Edwin