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Simplifying 256x4 + -81y4 = 0 Solving 256x4 + -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. 256x4 + -81y4 + 81y4 = 0 + 81y4 Combine like terms: -81y4 + 81y4 = 0 256x4 + 0 = 0 + 81y4 256x4 = 0 + 81y4 Remove the zero: 256x4 = 81y4 Divide each side by '256'. x4 = 0.31640625y4 Simplifying x4 = 0.31640625y4 Combine like terms: 0.31640625y4 + -0.31640625y4 = 0.00000000 x4 + -0.31640625y4 = 0.00000000 Factor a difference between two squares. (x2 + 0.5625y2)(x2 + -0.5625y2) = 0.00000000 Factor a difference between two squares. (x2 + 0.5625y2)((x + 0.75y)(x + -0.75y)) = 0.00000000Subproblem 1
Set the factor '(x2 + 0.5625y2)' equal to zero and attempt to solve: Simplifying x2 + 0.5625y2 = 0 Solving x2 + 0.5625y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.5625y2' to each side of the equation. x2 + 0.5625y2 + -0.5625y2 = 0 + -0.5625y2 Combine like terms: 0.5625y2 + -0.5625y2 = 0.0000 x2 + 0.0000 = 0 + -0.5625y2 x2 = 0 + -0.5625y2 Remove the zero: x2 = -0.5625y2 Simplifying x2 = -0.5625y2 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 + 0.75y)' equal to zero and attempt to solve: Simplifying x + 0.75y = 0 Solving x + 0.75y = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.75y' to each side of the equation. x + 0.75y + -0.75y = 0 + -0.75y Combine like terms: 0.75y + -0.75y = 0.00 x + 0.00 = 0 + -0.75y x = 0 + -0.75y Remove the zero: x = -0.75y Simplifying x = -0.75ySubproblem 3
Set the factor '(x + -0.75y)' equal to zero and attempt to solve: Simplifying x + -0.75y = 0 Solving x + -0.75y = 0 Move all terms containing x to the left, all other terms to the right. Add '0.75y' to each side of the equation. x + -0.75y + 0.75y = 0 + 0.75y Combine like terms: -0.75y + 0.75y = 0.00 x + 0.00 = 0 + 0.75y x = 0 + 0.75y Remove the zero: x = 0.75y Simplifying x = 0.75ySolution
x = {-0.75y, 0.75y}
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