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Simplifying 648x4 + -200x2y2 = 0 Reorder the terms: -200x2y2 + 648x4 = 0 Solving -200x2y2 + 648x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x2'. 8x2(-25y2 + 81x2) = 0 Factor a difference between two squares. 8x2((5y + 9x)(-5y + 9x)) = 0 Ignore the factor 8.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 '(5y + 9x)' equal to zero and attempt to solve: Simplifying 5y + 9x = 0 Reorder the terms: 9x + 5y = 0 Solving 9x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 9x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 9x + 0 = 0 + -5y 9x = 0 + -5y Remove the zero: 9x = -5y Divide each side by '9'. x = -0.5555555556y Simplifying x = -0.5555555556ySubproblem 3
Set the factor '(-5y + 9x)' equal to zero and attempt to solve: Simplifying -5y + 9x = 0 Reorder the terms: 9x + -5y = 0 Solving 9x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 9x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 9x + 0 = 0 + 5y 9x = 0 + 5y Remove the zero: 9x = 5y Divide each side by '9'. x = 0.5555555556y Simplifying x = 0.5555555556ySolution
x = {0, -0.5555555556y, 0.5555555556y}
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