25x^2-100xy+100y^2=0

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Solution for 25x^2-100xy+100y^2=0 equation:


Simplifying
25x2 + -100xy + 100y2 = 0

Reorder the terms:
-100xy + 25x2 + 100y2 = 0

Solving
-100xy + 25x2 + 100y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25'.
25(-4xy + x2 + 4y2) = 0

Factor a trinomial.
25((x + -2y)(x + -2y)) = 0

Ignore the factor 25.

Subproblem 1

Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2y

Subproblem 2

Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2y

Solution

x = {2y, 2y}

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