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Simplifying 16x4 + -81y8 = 0 Solving 16x4 + -81y8 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81y8' to each side of the equation. 16x4 + -81y8 + 81y8 = 0 + 81y8 Combine like terms: -81y8 + 81y8 = 0 16x4 + 0 = 0 + 81y8 16x4 = 0 + 81y8 Remove the zero: 16x4 = 81y8 Divide each side by '16'. x4 = 5.0625y8 Simplifying x4 = 5.0625y8 Combine like terms: 5.0625y8 + -5.0625y8 = 0.0000 x4 + -5.0625y8 = 0.0000 Factor a difference between two squares. (x2 + 2.25y4)(x2 + -2.25y4) = 0.0000 Factor a difference between two squares. (x2 + 2.25y4)((x + 1.5y2)(x + -1.5y2)) = 0.0000Subproblem 1
Set the factor '(x2 + 2.25y4)' equal to zero and attempt to solve: Simplifying x2 + 2.25y4 = 0 Solving x2 + 2.25y4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2.25y4' to each side of the equation. x2 + 2.25y4 + -2.25y4 = 0 + -2.25y4 Combine like terms: 2.25y4 + -2.25y4 = 0.00 x2 + 0.00 = 0 + -2.25y4 x2 = 0 + -2.25y4 Remove the zero: x2 = -2.25y4 Simplifying x2 = -2.25y4 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 + 1.5y2)' equal to zero and attempt to solve: Simplifying x + 1.5y2 = 0 Solving x + 1.5y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1.5y2' to each side of the equation. x + 1.5y2 + -1.5y2 = 0 + -1.5y2 Combine like terms: 1.5y2 + -1.5y2 = 0.0 x + 0.0 = 0 + -1.5y2 x = 0 + -1.5y2 Remove the zero: x = -1.5y2 Simplifying x = -1.5y2Subproblem 3
Set the factor '(x + -1.5y2)' equal to zero and attempt to solve: Simplifying x + -1.5y2 = 0 Solving x + -1.5y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1.5y2' to each side of the equation. x + -1.5y2 + 1.5y2 = 0 + 1.5y2 Combine like terms: -1.5y2 + 1.5y2 = 0.0 x + 0.0 = 0 + 1.5y2 x = 0 + 1.5y2 Remove the zero: x = 1.5y2 Simplifying x = 1.5y2Solution
x = {-1.5y2, 1.5y2}
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