X^4+9y^4=10

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Solution for X^4+9y^4=10 equation: 


Simplifying
X4 + 9y4 = 10

Solving
X4 + 9y4 = 10

Solving for variable 'X'.

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

Add '-9y4' to each side of the equation.
X4 + 9y4 + -9y4 = 10 + -9y4

Combine like terms: 9y4 + -9y4 = 0
X4 + 0 = 10 + -9y4
X4 = 10 + -9y4

Simplifying
X4 = 10 + -9y4

Reorder the terms:
-10 + X4 + 9y4 = 10 + -9y4 + -10 + 9y4

Reorder the terms:
-10 + X4 + 9y4 = 10 + -10 + -9y4 + 9y4

Combine like terms: 10 + -10 = 0
-10 + X4 + 9y4 = 0 + -9y4 + 9y4
-10 + X4 + 9y4 = -9y4 + 9y4

Combine like terms: -9y4 + 9y4 = 0
-10 + X4 + 9y4 = 0

Factor a trinomial.
(X2 + -9y2)(X2 + -1y2) = 0

Factor a difference between two squares.
((X + 3y)(X + -3y))(X2 + -1y2) = 0

Factor a difference between two squares.
((X + y)(X + -1y))(X + 3y)(X + -3y) = 0


Subproblem 1
Set the factor '(X + 3y)' equal to zero and attempt to solve:

Simplifying
X + 3y = 0

Solving
X + 3y = 0

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

Add '-3y' to each side of the equation.
X + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
X + 0 = 0 + -3y
X = 0 + -3y
Remove the zero:
X = -3y

Simplifying
X = -3y

Subproblem 2
Set the factor '(X + -3y)' equal to zero and attempt to solve:

Simplifying
X + -3y = 0

Solving
X + -3y = 0

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

Add '3y' to each side of the equation.
X + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
X + 0 = 0 + 3y
X = 0 + 3y
Remove the zero:
X = 3y

Simplifying
X = 3y

Subproblem 3
Set the factor '(X + y)' equal to zero and attempt to solve:

Simplifying
X + y = 0

Solving
X + y = 0

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

Add '-1y' to each side of the equation.
X + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
X + 0 = 0 + -1y
X = 0 + -1y
Remove the zero:
X = -1y

Simplifying
X = -1y

Subproblem 4
Set the factor '(X + -1y)' equal to zero and attempt to solve:

Simplifying
X + -1y = 0

Solving
X + -1y = 0

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

Add 'y' to each side of the equation.
X + -1y + y = 0 + y

Combine like terms: -1y + y = 0
X + 0 = 0 + y
X = 0 + y
Remove the zero:
X = y

Simplifying
X = y
Solution
X = {-3y, 3y, -1y, y}

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