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Simplifying 4x2 + 4xy2 + 4y4 = 0 Reorder the terms: 4xy2 + 4x2 + 4y4 = 0 Solving 4xy2 + 4x2 + 4y4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(xy2 + x2 + y4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(xy2 + x2 + y4)' equal to zero and attempt to solve: Simplifying xy2 + x2 + y4 = 0 Solving xy2 + x2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '-1y4' to each side of the equation. xy2 + x2 + y4 + -1y4 = 0 + -1y4 Combine like terms: y4 + -1y4 = 0 xy2 + x2 + 0 = 0 + -1y4 xy2 + x2 = 0 + -1y4 Remove the zero: xy2 + x2 = -1y4 The x term is xy2. 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. xy2 + x2 + 0.25y4 = -1y4 + 0.25y4 Combine like terms: -1y4 + 0.25y4 = -0.75y4 xy2 + x2 + 0.25y4 = -0.75y4 Factor a perfect square on the left side: (x + 0.5y2)(x + 0.5y2) = -0.75y4 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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