25x^4-20x^2y^2+4y^4=0

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Solution for 25x^4-20x^2y^2+4y^4=0 equation: 


Simplifying
25x4 + -20x2y2 + 4y4 = 0

Reorder the terms:
-20x2y2 + 25x4 + 4y4 = 0

Solving
-20x2y2 + 25x4 + 4y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x2 + -2y2)(5x2 + -2y2) = 0


Subproblem 1
Set the factor '(5x2 + -2y2)' equal to zero and attempt to solve:

Simplifying
5x2 + -2y2 = 0

Solving
5x2 + -2y2 = 0

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

Add '2y2' to each side of the equation.
5x2 + -2y2 + 2y2 = 0 + 2y2

Combine like terms: -2y2 + 2y2 = 0
5x2 + 0 = 0 + 2y2
5x2 = 0 + 2y2
Remove the zero:
5x2 = 2y2

Divide each side by '5'.
x2 = 0.4y2

Simplifying
x2 = 0.4y2

Take the square root of each side:
x = {-0.632455532y, 0.632455532y}

Subproblem 2
Set the factor '(5x2 + -2y2)' equal to zero and attempt to solve:

Simplifying
5x2 + -2y2 = 0

Solving
5x2 + -2y2 = 0

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

Add '2y2' to each side of the equation.
5x2 + -2y2 + 2y2 = 0 + 2y2

Combine like terms: -2y2 + 2y2 = 0
5x2 + 0 = 0 + 2y2
5x2 = 0 + 2y2
Remove the zero:
5x2 = 2y2

Divide each side by '5'.
x2 = 0.4y2

Simplifying
x2 = 0.4y2

Take the square root of each side:
x = {-0.632455532y, 0.632455532y}
Solution
x = {-0.632455532y, 0.632455532y, -0.632455532y, 0.632455532y}

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