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Simplifying X4 + -81y4 = 0 Solving X4 + -81y4 = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '81y4' to each side of the equation. X4 + -81y4 + 81y4 = 0 + 81y4 Combine like terms: -81y4 + 81y4 = 0 X4 + 0 = 0 + 81y4 X4 = 0 + 81y4 Remove the zero: X4 = 81y4 Simplifying X4 = 81y4 Combine like terms: 81y4 + -81y4 = 0 X4 + -81y4 = 0 Factor a difference between two squares. (X2 + 9y2)(X2 + -9y2) = 0 Factor a difference between two squares. (X2 + 9y2)((X + 3y)(X + -3y)) = 0Subproblem 1
Set the factor '(X2 + 9y2)' equal to zero and attempt to solve: Simplifying X2 + 9y2 = 0 Solving X2 + 9y2 = 0 Move all terms containing X to the left, all other terms to the right. Add '-9y2' to each side of the equation. X2 + 9y2 + -9y2 = 0 + -9y2 Combine like terms: 9y2 + -9y2 = 0 X2 + 0 = 0 + -9y2 X2 = 0 + -9y2 Remove the zero: X2 = -9y2 Simplifying X2 = -9y2 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 '(X + 3y)' equal to zero and attempt to solve: Simplifying X + 3y = 0 Solving X + 3y = 0 Move all terms containing X to the left, all other terms to the right. Add '-3y' to each side of the equation. X + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 X + 0 = 0 + -3y X = 0 + -3y Remove the zero: X = -3y Simplifying X = -3ySubproblem 3
Set the factor '(X + -3y)' equal to zero and attempt to solve: Simplifying X + -3y = 0 Solving X + -3y = 0 Move all terms containing X to the left, all other terms to the right. Add '3y' to each side of the equation. X + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 X + 0 = 0 + 3y X = 0 + 3y Remove the zero: X = 3y Simplifying X = 3ySolution
X = {-3y, 3y}
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