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Simplifying 2x3y + x2y2 + 4xy3 = 0 Reorder the terms: 4xy3 + x2y2 + 2x3y = 0 Solving 4xy3 + x2y2 + 2x3y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'xy'. xy(4y2 + xy + 2x2) = 0Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(4y2 + xy + 2x2)' equal to zero and attempt to solve: Simplifying 4y2 + xy + 2x2 = 0 Reorder the terms: xy + 2x2 + 4y2 = 0 Solving xy + 2x2 + 4y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5xy + x2 + 2y2 = 0 Move the constant term to the right: Add '-2y2' to each side of the equation. 0.5xy + x2 + 2y2 + -2y2 = 0 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0.5xy + x2 + 0 = 0 + -2y2 0.5xy + x2 = 0 + -2y2 Remove the zero: 0.5xy + 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. 0.5xy + x2 + 0.25y2 = -2y2 + 0.25y2 Combine like terms: -2y2 + 0.25y2 = -1.75y2 0.5xy + x2 + 0.25y2 = -1.75y2 Factor a perfect square on the left side: (x + 0.5y)(x + 0.5y) = -1.75y2 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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