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Simplifying 8x2 + -20xy + 8y2 = 0 Reorder the terms: -20xy + 8x2 + 8y2 = 0 Solving -20xy + 8x2 + 8y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5xy + 2x2 + 2y2) = 0 Factor a trinomial. 4((x + -2y)(2x + -1y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySubproblem 2
Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 2x + 0 = 0 + y 2x = 0 + y Remove the zero: 2x = y Divide each side by '2'. x = 0.5y Simplifying x = 0.5ySolution
x = {2y, 0.5y}
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