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Simplifying 6x * x + 11xy + 5y * y = 0 Multiply x * x 6x2 + 11xy + 5y * y = 0 Multiply y * y 6x2 + 11xy + 5y2 = 0 Reorder the terms: 11xy + 6x2 + 5y2 = 0 Solving 11xy + 6x2 + 5y2 = 0 Solving for variable 'x'. Factor a trinomial. (6x + 5y)(x + y) = 0Subproblem 1
Set the factor '(6x + 5y)' equal to zero and attempt to solve: Simplifying 6x + 5y = 0 Solving 6x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 6x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 6x + 0 = 0 + -5y 6x = 0 + -5y Remove the zero: 6x = -5y Divide each side by '6'. x = -0.8333333333y Simplifying x = -0.8333333333ySubproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySolution
x = {-0.8333333333y, -1y}
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