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Simplifying 25x4 + 45x3y + -10x2y2 = 0 Reorder the terms: -10x2y2 + 45x3y + 25x4 = 0 Solving -10x2y2 + 45x3y + 25x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(-2y2 + 9xy + 5x2) = 0 Factor a trinomial. 5x2((-2y + -1x)(y + -5x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-2y + -1x)' equal to zero and attempt to solve: Simplifying -2y + -1x = 0 Reorder the terms: -1x + -2y = 0 Solving -1x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. -1x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 -1x + 0 = 0 + 2y -1x = 0 + 2y Remove the zero: -1x = 2y Divide each side by '-1'. x = -2y Simplifying x = -2ySubproblem 3
Set the factor '(y + -5x)' equal to zero and attempt to solve: Simplifying y + -5x = 0 Reorder the terms: -5x + y = 0 Solving -5x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -5x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -5x + 0 = 0 + -1y -5x = 0 + -1y Remove the zero: -5x = -1y Divide each side by '-5'. x = 0.2y Simplifying x = 0.2ySolution
x = {0, -2y, 0.2y}
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