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Simplifying 40x2 + 130xy + -225y2 = 0 Reorder the terms: 130xy + 40x2 + -225y2 = 0 Solving 130xy + 40x2 + -225y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(26xy + 8x2 + -45y2) = 0 Factor a trinomial. 5((4x + -5y)(2x + 9y)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4x + -5y)' equal to zero and attempt to solve: Simplifying 4x + -5y = 0 Solving 4x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 4x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 4x + 0 = 0 + 5y 4x = 0 + 5y Remove the zero: 4x = 5y Divide each side by '4'. x = 1.25y Simplifying x = 1.25ySubproblem 2
Set the factor '(2x + 9y)' equal to zero and attempt to solve: Simplifying 2x + 9y = 0 Solving 2x + 9y = 0 Move all terms containing x to the left, all other terms to the right. Add '-9y' to each side of the equation. 2x + 9y + -9y = 0 + -9y Combine like terms: 9y + -9y = 0 2x + 0 = 0 + -9y 2x = 0 + -9y Remove the zero: 2x = -9y Divide each side by '2'. x = -4.5y Simplifying x = -4.5ySolution
x = {1.25y, -4.5y}
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