Solve for y: 2x^2 - 3xy - 4y^2 = 5

Question

i divided by 2 first to get x^2 - 3/2xy -2y^2 = 5/2  now complete the square?  I keep getting stuck with a variable in xy I cannot isolate y...

Answer 1

here is the solution:

2x^2 - 3xy -4y^2 -5 = 0

-4y^2 -3xy + 2x^2 -5 = 0

4y^2 - 3xy - 2x^2 + 5 = 0   multiply through by -1

a = 4, b = 3x, c - (-2x^2 +5)

use quadratic equation:

y = -(-3x) +or- sqrt[9x^2 - 4*4*(-2x^2 +5)]

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

                                 2*4

y = 3x + or - sqrt [9x^2 - 26(-2x^2 +5)]

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

                            8

y = 3x + or - sqrt[ 9x^2 +32x^2 - 80]

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

                                8

y = 3x + or - sqrt(41x^2 -80)

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

                        8

thank you Ann Marie