16x^4y-y^5=0

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Solution for 16x^4y-y^5=0 equation:


Simplifying
16x4y + -1y5 = 0

Solving
16x4y + -1y5 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add 'y5' to each side of the equation.
16x4y + -1y5 + y5 = 0 + y5

Combine like terms: -1y5 + y5 = 0
16x4y + 0 = 0 + y5
16x4y = 0 + y5
Remove the zero:
16x4y = y5

Divide each side by '16y'.
x4 = 0.0625y4

Simplifying
x4 = 0.0625y4

Combine like terms: 0.0625y4 + -0.0625y4 = 0.0000
x4 + -0.0625y4 = 0.0000

Factor a difference between two squares.
(x2 + 0.25y2)(x2 + -0.25y2) = 0.0000

Factor a difference between two squares.
(x2 + 0.25y2)((x + 0.5y)(x + -0.5y)) = 0.0000

Subproblem 1

Set the factor '(x2 + 0.25y2)' equal to zero and attempt to solve: Simplifying x2 + 0.25y2 = 0 Solving x2 + 0.25y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.25y2' to each side of the equation. x2 + 0.25y2 + -0.25y2 = 0 + -0.25y2 Combine like terms: 0.25y2 + -0.25y2 = 0.00 x2 + 0.00 = 0 + -0.25y2 x2 = 0 + -0.25y2 Remove the zero: x2 = -0.25y2 Simplifying x2 = -0.25y2 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 + 0.5y)' equal to zero and attempt to solve: Simplifying x + 0.5y = 0 Solving x + 0.5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-0.5y' to each side of the equation. x + 0.5y + -0.5y = 0 + -0.5y Combine like terms: 0.5y + -0.5y = 0.0 x + 0.0 = 0 + -0.5y x = 0 + -0.5y Remove the zero: x = -0.5y Simplifying x = -0.5y

Subproblem 3

Set the factor '(x + -0.5y)' equal to zero and attempt to solve: Simplifying x + -0.5y = 0 Solving x + -0.5y = 0 Move all terms containing x to the left, all other terms to the right. Add '0.5y' to each side of the equation. x + -0.5y + 0.5y = 0 + 0.5y Combine like terms: -0.5y + 0.5y = 0.0 x + 0.0 = 0 + 0.5y x = 0 + 0.5y Remove the zero: x = 0.5y Simplifying x = 0.5y

Solution

x = {-0.5y, 0.5y}

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