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Simplifying 150x4 + -54x2y2 = 0 Reorder the terms: -54x2y2 + 150x4 = 0 Solving -54x2y2 + 150x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x2'. 6x2(-9y2 + 25x2) = 0 Factor a difference between two squares. 6x2((3y + 5x)(-3y + 5x)) = 0 Ignore the factor 6.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 '(3y + 5x)' equal to zero and attempt to solve: Simplifying 3y + 5x = 0 Reorder the terms: 5x + 3y = 0 Solving 5x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 5x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 5x + 0 = 0 + -3y 5x = 0 + -3y Remove the zero: 5x = -3y Divide each side by '5'. x = -0.6y Simplifying x = -0.6ySubproblem 3
Set the factor '(-3y + 5x)' equal to zero and attempt to solve: Simplifying -3y + 5x = 0 Reorder the terms: 5x + -3y = 0 Solving 5x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 5x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 5x + 0 = 0 + 3y 5x = 0 + 3y Remove the zero: 5x = 3y Divide each side by '5'. x = 0.6y Simplifying x = 0.6ySolution
x = {0, -0.6y, 0.6y}
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