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Simplifying 1024x4 + -4y4 = 0 Solving 1024x4 + -4y4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4y4' to each side of the equation. 1024x4 + -4y4 + 4y4 = 0 + 4y4 Combine like terms: -4y4 + 4y4 = 0 1024x4 + 0 = 0 + 4y4 1024x4 = 0 + 4y4 Remove the zero: 1024x4 = 4y4 Divide each side by '1024'. x4 = 0.00390625y4 Simplifying x4 = 0.00390625y4 Combine like terms: 0.00390625y4 + -0.00390625y4 = 0.00000000 x4 + -0.00390625y4 = 0.00000000 Factor a difference between two squares. (x2 + 0.0625y2)(x2 + -0.0625y2) = 0.00000000 Factor a difference between two squares. (x2 + 0.0625y2)((x + 0.25y)(x + -0.25y)) = 0.00000000Subproblem 1
Set the factor '(x2 + 0.0625y2)' equal to zero and attempt to solve: Simplifying x2 + 0.0625y2 = 0 Solving x2 + 0.0625y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.0625y2' to each side of the equation. x2 + 0.0625y2 + -0.0625y2 = 0 + -0.0625y2 Combine like terms: 0.0625y2 + -0.0625y2 = 0.0000 x2 + 0.0000 = 0 + -0.0625y2 x2 = 0 + -0.0625y2 Remove the zero: x2 = -0.0625y2 Simplifying x2 = -0.0625y2 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 + 0.25y)' equal to zero and attempt to solve: Simplifying x + 0.25y = 0 Solving x + 0.25y = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.25y' to each side of the equation. x + 0.25y + -0.25y = 0 + -0.25y Combine like terms: 0.25y + -0.25y = 0.00 x + 0.00 = 0 + -0.25y x = 0 + -0.25y Remove the zero: x = -0.25y Simplifying x = -0.25ySubproblem 3
Set the factor '(x + -0.25y)' equal to zero and attempt to solve: Simplifying x + -0.25y = 0 Solving x + -0.25y = 0 Move all terms containing x to the left, all other terms to the right. Add '0.25y' to each side of the equation. x + -0.25y + 0.25y = 0 + 0.25y Combine like terms: -0.25y + 0.25y = 0.00 x + 0.00 = 0 + 0.25y x = 0 + 0.25y Remove the zero: x = 0.25y Simplifying x = 0.25ySolution
x = {-0.25y, 0.25y}
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