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Simplifying 42x2 + 186xy + 180y2 = 0 Reorder the terms: 186xy + 42x2 + 180y2 = 0 Solving 186xy + 42x2 + 180y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(31xy + 7x2 + 30y2) = 0 Factor a trinomial. 6((7x + 10y)(x + 3y)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7x + 10y)' equal to zero and attempt to solve: Simplifying 7x + 10y = 0 Solving 7x + 10y = 0 Move all terms containing x to the left, all other terms to the right. Add '-10y' to each side of the equation. 7x + 10y + -10y = 0 + -10y Combine like terms: 10y + -10y = 0 7x + 0 = 0 + -10y 7x = 0 + -10y Remove the zero: 7x = -10y Divide each side by '7'. x = -1.428571429y Simplifying x = -1.428571429ySubproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySolution
x = {-1.428571429y, -3y}
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