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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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