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Simplifying 10x2 + 39xy + -27y2 = 0 Reorder the terms: 39xy + 10x2 + -27y2 = 0 Solving 39xy + 10x2 + -27y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -3y)(2x + 9y) = 0Subproblem 1
Set the factor '(5x + -3y)' equal to zero and attempt to solve: Simplifying 5x + -3y = 0 Solving 5x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 5x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 5x + 0 = 0 + 3y 5x = 0 + 3y Remove the zero: 5x = 3y Divide each side by '5'. x = 0.6y Simplifying x = 0.6ySubproblem 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 = {0.6y, -4.5y}
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