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Simplifying 42x2 + -11xy + -20y2 = 0 Reorder the terms: -11xy + 42x2 + -20y2 = 0 Solving -11xy + 42x2 + -20y2 = 0 Solving for variable 'x'. Factor a trinomial. (6x + -5y)(7x + 4y) = 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 '(7x + 4y)' equal to zero and attempt to solve: Simplifying 7x + 4y = 0 Solving 7x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 7x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 7x + 0 = 0 + -4y 7x = 0 + -4y Remove the zero: 7x = -4y Divide each side by '7'. x = -0.5714285714y Simplifying x = -0.5714285714ySolution
x = {0.8333333333y, -0.5714285714y}
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