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Simplifying x2 + 3xy + y2 + 2x2 + 5xy + -1y2 = 0 Reorder the terms: 3xy + 5xy + x2 + 2x2 + y2 + -1y2 = 0 Combine like terms: 3xy + 5xy = 8xy 8xy + x2 + 2x2 + y2 + -1y2 = 0 Combine like terms: x2 + 2x2 = 3x2 8xy + 3x2 + y2 + -1y2 = 0 Combine like terms: y2 + -1y2 = 0 8xy + 3x2 + 0 = 0 8xy + 3x2 = 0 Solving 8xy + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(8y + 3x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(8y + 3x)' equal to zero and attempt to solve: Simplifying 8y + 3x = 0 Reorder the terms: 3x + 8y = 0 Solving 3x + 8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-8y' to each side of the equation. 3x + 8y + -8y = 0 + -8y Combine like terms: 8y + -8y = 0 3x + 0 = 0 + -8y 3x = 0 + -8y Remove the zero: 3x = -8y Divide each side by '3'. x = -2.666666667y Simplifying x = -2.666666667ySolution
x = {0, -2.666666667y}
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