16x^4-81y^4=0

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Solution for 16x^4-81y^4=0 equation:


Simplifying
16x4 + -81y4 = 0

Solving
16x4 + -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.
16x4 + -81y4 + 81y4 = 0 + 81y4

Combine like terms: -81y4 + 81y4 = 0
16x4 + 0 = 0 + 81y4
16x4 = 0 + 81y4
Remove the zero:
16x4 = 81y4

Divide each side by '16'.
x4 = 5.0625y4

Simplifying
x4 = 5.0625y4

Combine like terms: 5.0625y4 + -5.0625y4 = 0.0000
x4 + -5.0625y4 = 0.0000

Factor a difference between two squares.
(x2 + 2.25y2)(x2 + -2.25y2) = 0.0000

Factor a difference between two squares.
(x2 + 2.25y2)((x + 1.5y)(x + -1.5y)) = 0.0000

Subproblem 1

Set the factor '(x2 + 2.25y2)' equal to zero and attempt to solve: Simplifying x2 + 2.25y2 = 0 Solving x2 + 2.25y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2.25y2' to each side of the equation. x2 + 2.25y2 + -2.25y2 = 0 + -2.25y2 Combine like terms: 2.25y2 + -2.25y2 = 0.00 x2 + 0.00 = 0 + -2.25y2 x2 = 0 + -2.25y2 Remove the zero: x2 = -2.25y2 Simplifying x2 = -2.25y2 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 + 1.5y)' equal to zero and attempt to solve: Simplifying x + 1.5y = 0 Solving x + 1.5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1.5y' to each side of the equation. x + 1.5y + -1.5y = 0 + -1.5y Combine like terms: 1.5y + -1.5y = 0.0 x + 0.0 = 0 + -1.5y x = 0 + -1.5y Remove the zero: x = -1.5y Simplifying x = -1.5y

Subproblem 3

Set the factor '(x + -1.5y)' equal to zero and attempt to solve: Simplifying x + -1.5y = 0 Solving x + -1.5y = 0 Move all terms containing x to the left, all other terms to the right. Add '1.5y' to each side of the equation. x + -1.5y + 1.5y = 0 + 1.5y Combine like terms: -1.5y + 1.5y = 0.0 x + 0.0 = 0 + 1.5y x = 0 + 1.5y Remove the zero: x = 1.5y Simplifying x = 1.5y

Solution

x = {-1.5y, 1.5y}

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