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Simplifying 5x2 + 19xy + 12y2 = 0 Reorder the terms: 19xy + 5x2 + 12y2 = 0 Solving 19xy + 5x2 + 12y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + 4y)(x + 3y) = 0Subproblem 1
Set the factor '(5x + 4y)' equal to zero and attempt to solve: Simplifying 5x + 4y = 0 Solving 5x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 5x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 5x + 0 = 0 + -4y 5x = 0 + -4y Remove the zero: 5x = -4y Divide each side by '5'. x = -0.8y Simplifying x = -0.8ySubproblem 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 = {-0.8y, -3y}
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