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Simplifying 20x2 + -10xy + -10y2 = 0 Reorder the terms: -10xy + 20x2 + -10y2 = 0 Solving -10xy + 20x2 + -10y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-1xy + 2x2 + -1y2) = 0 Factor a trinomial. 10((x + -1y)(2x + y)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySubproblem 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 = {y, -0.5y}
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