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Simplifying 625x4 + -256y4 = 0 Solving 625x4 + -256y4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '256y4' to each side of the equation. 625x4 + -256y4 + 256y4 = 0 + 256y4 Combine like terms: -256y4 + 256y4 = 0 625x4 + 0 = 0 + 256y4 625x4 = 0 + 256y4 Remove the zero: 625x4 = 256y4 Divide each side by '625'. x4 = 0.4096y4 Simplifying x4 = 0.4096y4 Combine like terms: 0.4096y4 + -0.4096y4 = 0.0000 x4 + -0.4096y4 = 0.0000 Factor a difference between two squares. (x2 + 0.64y2)(x2 + -0.64y2) = 0.0000 Factor a difference between two squares. (x2 + 0.64y2)((x + 0.8y)(x + -0.8y)) = 0.0000Subproblem 1
Set the factor '(x2 + 0.64y2)' equal to zero and attempt to solve: Simplifying x2 + 0.64y2 = 0 Solving x2 + 0.64y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.64y2' to each side of the equation. x2 + 0.64y2 + -0.64y2 = 0 + -0.64y2 Combine like terms: 0.64y2 + -0.64y2 = 0.00 x2 + 0.00 = 0 + -0.64y2 x2 = 0 + -0.64y2 Remove the zero: x2 = -0.64y2 Simplifying x2 = -0.64y2 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 + 0.8y)' equal to zero and attempt to solve: Simplifying x + 0.8y = 0 Solving x + 0.8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.8y' to each side of the equation. x + 0.8y + -0.8y = 0 + -0.8y Combine like terms: 0.8y + -0.8y = 0.0 x + 0.0 = 0 + -0.8y x = 0 + -0.8y Remove the zero: x = -0.8y Simplifying x = -0.8ySubproblem 3
Set the factor '(x + -0.8y)' equal to zero and attempt to solve: Simplifying x + -0.8y = 0 Solving x + -0.8y = 0 Move all terms containing x to the left, all other terms to the right. Add '0.8y' to each side of the equation. x + -0.8y + 0.8y = 0 + 0.8y Combine like terms: -0.8y + 0.8y = 0.0 x + 0.0 = 0 + 0.8y x = 0 + 0.8y Remove the zero: x = 0.8y Simplifying x = 0.8ySolution
x = {-0.8y, 0.8y}
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