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Simplifying 7xy6 + 2x3y4 + 2x5y2 = 0 Solving 7xy6 + 2x3y4 + 2x5y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'xy2'. xy2(7y4 + 2x2y2 + 2x4) = 0Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve: Simplifying xy2 = 0 Solving xy2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy2 = 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 '(7y4 + 2x2y2 + 2x4)' equal to zero and attempt to solve: Simplifying 7y4 + 2x2y2 + 2x4 = 0 Reorder the terms: 2x2y2 + 2x4 + 7y4 = 0 Solving 2x2y2 + 2x4 + 7y4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. x2y2 + x4 + 3.5y4 = 0 Move the constant term to the right: Add '-3.5y4' to each side of the equation. x2y2 + x4 + 3.5y4 + -3.5y4 = 0 + -3.5y4 Combine like terms: 3.5y4 + -3.5y4 = 0.0 x2y2 + x4 + 0.0 = 0 + -3.5y4 x2y2 + x4 = 0 + -3.5y4 Remove the zero: x2y2 + x4 = -3.5y4 The x term is x2y2. Take half its coefficient (0.5y2). Square it (0.25y4) and add it to both sides. Add '0.25y4' to each side of the equation. y4 + x4 + 0.25y4 = -3.5y4 + 0.25y4 Reorder the terms: x4 + y4 + 0.25y4 = -3.5y4 + 0.25y4 Combine like terms: y4 + 0.25y4 = 1.25y4 x4 + 1.25y4 = -3.5y4 + 0.25y4 Combine like terms: -3.5y4 + 0.25y4 = -3.25y4 x4 + 1.25y4 = -3.25y4 Factor a perfect square on the left side: (x2 + 0.5y2)(x2 + 0.5y2) = -3.25y4 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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