4x^2+xy+-9y^2=0

Simple and best practice solution for 4x^2+xy+-9y^2=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4x^2+xy+-9y^2=0 equation: 


Simplifying
4x2 + xy + -9y2 = 0

Reorder the terms:
xy + 4x2 + -9y2 = 0

Solving
xy + 4x2 + -9y2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.25xy + x2 + -2.25y2 = 0

Move the constant term to the right:

Add '2.25y2' to each side of the equation.
0.25xy + x2 + -2.25y2 + 2.25y2 = 0 + 2.25y2

Combine like terms: -2.25y2 + 2.25y2 = 0.00
0.25xy + x2 + 0.00 = 0 + 2.25y2
0.25xy + x2 = 0 + 2.25y2
Remove the zero:
0.25xy + x2 = 2.25y2

The x term is xy.  Take half its coefficient (0.5y).
Square it (0.25y2) and add it to both sides.

Add '0.25y2' to each side of the equation.
0.25xy + x2 + 0.25y2 = 2.25y2 + 0.25y2

Combine like terms: 2.25y2 + 0.25y2 = 2.5y2
0.25xy + x2 + 0.25y2 = 2.5y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = 2.5y2

Calculate the square root of the right side: 1.58113883y

Break this problem into two subproblems by setting 
(x + 0.5y) equal to 1.58113883y and -1.58113883y.


Subproblem 1
x + 0.5y = 1.58113883y

Simplifying
x + 0.5y = 1.58113883y

Solving
x + 0.5y = 1.58113883y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5y' to each side of the equation.
x + 0.5y + -0.5y = 1.58113883y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = 1.58113883y + -0.5y
x = 1.58113883y + -0.5y

Combine like terms: 1.58113883y + -0.5y = 1.08113883y
x = 1.08113883y

Simplifying
x = 1.08113883y


Subproblem 2
x + 0.5y = -1.58113883y

Simplifying
x + 0.5y = -1.58113883y

Solving
x + 0.5y = -1.58113883y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5y' to each side of the equation.
x + 0.5y + -0.5y = -1.58113883y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = -1.58113883y + -0.5y
x = -1.58113883y + -0.5y

Combine like terms: -1.58113883y + -0.5y = -2.08113883y
x = -2.08113883y

Simplifying
x = -2.08113883y


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.08113883y, -2.08113883y}

See similar equations:

| 4-5(4+5v)=36+v | | 6+13x-1=7x+1 | | -5(r+7)=-85 | | 5(-7+4x)=30+7x | | 14=2n+8 | | 2x^4+x-1=0 | | -24-7m=-6(2m-1) | | x^3+3x^2y+y^2= | | -2k-5(5k-3)=-8k-23 | | 2.9x=-52.2 | | 6(c+8+12)=53 | | -8(7b+5)=-40+8b | | 5x^2=20-15x | | -36-8x=3x-5(2x+8) | | 6*c=53+8+12 | | 5r-6r-7s= | | 6+c+8+12=53 | | 8(7-4x)=-2-3x | | 5+3x+7x=-25 | | -6(4r-8)=-8r | | 6*c=53-(8+12) | | 4+x-5x=16 | | 3y^2-8y+4= | | s=-5t^2+17t+12 | | -7(4x-4)-5=3x-39 | | 2(x+8)+8=2x+3 | | f(4)=2x^2-x+9 | | -33+7r=3(-3+5r) | | 8x-3x=4+6x | | 67=5x+4x-5 | | 8+7m=8(1+8m)+4m | | 3x-3+5x=27 |

Equations solver categories