(x^2+3xy+4y^2)+(6x^2-2xy+2y^2)+(3x^2-xy-8y^2)=

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Solution for (x^2+3xy+4y^2)+(6x^2-2xy+2y^2)+(3x^2-xy-8y^2)= equation: 


Simplifying
(x2 + 3xy + 4y2) + (6x2 + -2xy + 2y2) + (3x2 + -1xy + -8y2) = 0

Reorder the terms:
(3xy + x2 + 4y2) + (6x2 + -2xy + 2y2) + (3x2 + -1xy + -8y2) = 0

Remove parenthesis around (3xy + x2 + 4y2)
3xy + x2 + 4y2 + (6x2 + -2xy + 2y2) + (3x2 + -1xy + -8y2) = 0

Reorder the terms:
3xy + x2 + 4y2 + (-2xy + 6x2 + 2y2) + (3x2 + -1xy + -8y2) = 0

Remove parenthesis around (-2xy + 6x2 + 2y2)
3xy + x2 + 4y2 + -2xy + 6x2 + 2y2 + (3x2 + -1xy + -8y2) = 0

Reorder the terms:
3xy + x2 + 4y2 + -2xy + 6x2 + 2y2 + (-1xy + 3x2 + -8y2) = 0

Remove parenthesis around (-1xy + 3x2 + -8y2)
3xy + x2 + 4y2 + -2xy + 6x2 + 2y2 + -1xy + 3x2 + -8y2 = 0

Reorder the terms:
3xy + -2xy + -1xy + x2 + 6x2 + 3x2 + 4y2 + 2y2 + -8y2 = 0

Combine like terms: 3xy + -2xy = 1xy
1xy + -1xy + x2 + 6x2 + 3x2 + 4y2 + 2y2 + -8y2 = 0

Combine like terms: 1xy + -1xy = 0
0 + x2 + 6x2 + 3x2 + 4y2 + 2y2 + -8y2 = 0
x2 + 6x2 + 3x2 + 4y2 + 2y2 + -8y2 = 0

Combine like terms: x2 + 6x2 = 7x2
7x2 + 3x2 + 4y2 + 2y2 + -8y2 = 0

Combine like terms: 7x2 + 3x2 = 10x2
10x2 + 4y2 + 2y2 + -8y2 = 0

Combine like terms: 4y2 + 2y2 = 6y2
10x2 + 6y2 + -8y2 = 0

Combine like terms: 6y2 + -8y2 = -2y2
10x2 + -2y2 = 0

Solving
10x2 + -2y2 = 0

Solving for variable 'x'.

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

Add '2y2' to each side of the equation.
10x2 + -2y2 + 2y2 = 0 + 2y2

Combine like terms: -2y2 + 2y2 = 0
10x2 + 0 = 0 + 2y2
10x2 = 0 + 2y2
Remove the zero:
10x2 = 2y2

Divide each side by '10'.
x2 = 0.2y2

Simplifying
x2 = 0.2y2

Take the square root of each side:
x = {-0.447213596y, 0.447213596y}

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