9x^2+3xy-18y^2=0

Simple and best practice solution for 9x^2+3xy-18y^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 9x^2+3xy-18y^2=0 equation: 


Simplifying
9x2 + 3xy + -18y2 = 0

Reorder the terms:
3xy + 9x2 + -18y2 = 0

Solving
3xy + 9x2 + -18y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(xy + 3x2 + -6y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(xy + 3x2 + -6y2)' equal to zero and attempt to solve:

Simplifying
xy + 3x2 + -6y2 = 0

Solving
xy + 3x2 + -6y2 = 0

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

Divide each side by '3'.
0.3333333333xy + x2 + -2y2 = 0

Move the constant term to the right:

Add '2y2' to each side of the equation.
0.3333333333xy + x2 + -2y2 + 2y2 = 0 + 2y2

Combine like terms: -2y2 + 2y2 = 0
0.3333333333xy + x2 + 0 = 0 + 2y2
0.3333333333xy + x2 = 0 + 2y2
Remove the zero:
0.3333333333xy + x2 = 2y2

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.
0.3333333333xy + x2 + 0.25y2 = 2y2 + 0.25y2

Combine like terms: 2y2 + 0.25y2 = 2.25y2
0.3333333333xy + x2 + 0.25y2 = 2.25y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = 2.25y2

Calculate the square root of the right side: 1.5y

Break this problem into two subproblems by setting 
(x + 0.5y) equal to 1.5y and -1.5y.


Subproblem 1
x + 0.5y = 1.5y

Simplifying
x + 0.5y = 1.5y

Solving
x + 0.5y = 1.5y

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 = 1.5y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = 1.5y + -0.5y
x = 1.5y + -0.5y

Combine like terms: 1.5y + -0.5y = 1y
x = 1y

Simplifying
x = 1y


Subproblem 2
x + 0.5y = -1.5y

Simplifying
x + 0.5y = -1.5y

Solving
x + 0.5y = -1.5y

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 = -1.5y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = -1.5y + -0.5y
x = -1.5y + -0.5y

Combine like terms: -1.5y + -0.5y = -2y
x = -2y

Simplifying
x = -2y


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1y, -2y}
Solution
x = {1y, -2y}

See similar equations:

| Cos(40)=7/x | | 0=(3x-5)(2x+4) | | 28x=-84 | | -3+9=3 | | 15-B=10 | | c^2+30=90 | | -4/-1 | | lnx+ln(x-2)=ln(5x) | | 2(3x-1)+3(2x-1)=3.4 | | 4y+13=10+2y | | n^3-3n^2+2n=504 | | n^3-3n^2+2n=0 | | lgx-lg(3x-1)=2 | | n^3-n^2+2n=0 | | -10/12 | | 13-14x=29 | | 7-A=3 | | 10.8x+39.57=-9.2x+38.51 | | 6.9x-2.3=11.5 | | -(z+8)+(5z+1)=-4(z+1) | | 3t+6t+8t=17t | | x^(9/2)e^(x) | | 4(8-3x)=-52 | | 2(2*x)=5(11-3x) | | 0.5y=x-1.5 | | 11m+6n-3m+9n= | | 2(-3+2x)=14 | | X^(9/7)/X^2 | | 7(4x-3)=109 | | 7x-5=10x-2 | | -(z+9)+(5z+1)=-7(z+1) | | 4y=-x+6 |

Equations solver categories