(5x^2-xy-y^2)+(x^2+7xy+3y^2)=

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Solution for (5x^2-xy-y^2)+(x^2+7xy+3y^2)= equation: 


Simplifying
(5x2 + -1xy + -1y2) + (x2 + 7xy + 3y2) = 0

Reorder the terms:
(-1xy + 5x2 + -1y2) + (x2 + 7xy + 3y2) = 0

Remove parenthesis around (-1xy + 5x2 + -1y2)
-1xy + 5x2 + -1y2 + (x2 + 7xy + 3y2) = 0

Reorder the terms:
-1xy + 5x2 + -1y2 + (7xy + x2 + 3y2) = 0

Remove parenthesis around (7xy + x2 + 3y2)
-1xy + 5x2 + -1y2 + 7xy + x2 + 3y2 = 0

Reorder the terms:
-1xy + 7xy + 5x2 + x2 + -1y2 + 3y2 = 0

Combine like terms: -1xy + 7xy = 6xy
6xy + 5x2 + x2 + -1y2 + 3y2 = 0

Combine like terms: 5x2 + x2 = 6x2
6xy + 6x2 + -1y2 + 3y2 = 0

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

Solving
6xy + 6x2 + 2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3xy + 3x2 + y2) = 0

Ignore the factor 2.

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

Simplifying
3xy + 3x2 + y2 = 0

Solving
3xy + 3x2 + y2 = 0

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

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

Move the constant term to the right:

Add '-1y2' to each side of the equation.
xy + x2 + 0.3333333333y2 + -1y2 = 0 + -1y2

Combine like terms: 0.3333333333y2 + -1y2 = -0.6666666667y2
xy + x2 + -0.6666666667y2 = 0 + -1y2
Remove the zero:
xy + x2 + -0.6666666667y2 = -1y2

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.
y2 + x2 + -0.6666666667y2 + 0.25y2 = -1y2 + 0.25y2

Reorder the terms:
x2 + y2 + -0.6666666667y2 + 0.25y2 = -1y2 + 0.25y2

Combine like terms: y2 + -0.6666666667y2 = 0.3333333333y2
x2 + 0.3333333333y2 + 0.25y2 = -1y2 + 0.25y2

Combine like terms: 0.3333333333y2 + 0.25y2 = 0.5833333333y2
x2 + 0.5833333333y2 = -1y2 + 0.25y2

Combine like terms: -1y2 + 0.25y2 = -0.75y2
x2 + 0.5833333333y2 = -0.75y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = -0.75y2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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