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Simplifying 2x2 + -8xy + xy + -4y2 = 0 Reorder the terms: -8xy + xy + 2x2 + -4y2 = 0 Combine like terms: -8xy + xy = -7xy -7xy + 2x2 + -4y2 = 0 Solving -7xy + 2x2 + -4y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -4y)(2x + y) = 0Subproblem 1
Set the factor '(x + -4y)' equal to zero and attempt to solve: Simplifying x + -4y = 0 Solving x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 x + 0 = 0 + 4y x = 0 + 4y Remove the zero: x = 4y Simplifying x = 4ySubproblem 2
Set the factor '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySolution
x = {4y, -0.5y}
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