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Simplifying x4 + -16y4 = 0 Solving x4 + -16y4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16y4' to each side of the equation. x4 + -16y4 + 16y4 = 0 + 16y4 Combine like terms: -16y4 + 16y4 = 0 x4 + 0 = 0 + 16y4 x4 = 0 + 16y4 Remove the zero: x4 = 16y4 Simplifying x4 = 16y4 Combine like terms: 16y4 + -16y4 = 0 x4 + -16y4 = 0 Factor a difference between two squares. (x2 + 4y2)(x2 + -4y2) = 0 Factor a difference between two squares. (x2 + 4y2)((x + 2y)(x + -2y)) = 0Subproblem 1
Set the factor '(x2 + 4y2)' equal to zero and attempt to solve: Simplifying x2 + 4y2 = 0 Solving x2 + 4y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y2' to each side of the equation. x2 + 4y2 + -4y2 = 0 + -4y2 Combine like terms: 4y2 + -4y2 = 0 x2 + 0 = 0 + -4y2 x2 = 0 + -4y2 Remove the zero: x2 = -4y2 Simplifying x2 = -4y2 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 + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 0 + -2y x = 0 + -2y Remove the zero: x = -2y Simplifying x = -2ySubproblem 3
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySolution
x = {-2y, 2y}
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