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Simplifying 30x2 + 58xy + -28y2 = 0 Reorder the terms: 58xy + 30x2 + -28y2 = 0 Solving 58xy + 30x2 + -28y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(29xy + 15x2 + -14y2) = 0 Factor a trinomial. 2((5x + -2y)(3x + 7y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5x + -2y)' equal to zero and attempt to solve: Simplifying 5x + -2y = 0 Solving 5x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 5x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 5x + 0 = 0 + 2y 5x = 0 + 2y Remove the zero: 5x = 2y Divide each side by '5'. x = 0.4y Simplifying x = 0.4ySubproblem 2
Set the factor '(3x + 7y)' equal to zero and attempt to solve: Simplifying 3x + 7y = 0 Solving 3x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 3x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 3x + 0 = 0 + -7y 3x = 0 + -7y Remove the zero: 3x = -7y Divide each side by '3'. x = -2.333333333y Simplifying x = -2.333333333ySolution
x = {0.4y, -2.333333333y}
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