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Simplifying 2cos(2x + -1y) * dx + -1cos(2x + -1y) * dy = 0 Reorder the terms for easier multiplication: 2cos * dx(2x + -1y) + -1cos(2x + -1y) * dy = 0 Multiply cos * dx 2cdosx(2x + -1y) + -1cos(2x + -1y) * dy = 0 (2x * 2cdosx + -1y * 2cdosx) + -1cos(2x + -1y) * dy = 0 Reorder the terms: (-2cdosxy + 4cdosx2) + -1cos(2x + -1y) * dy = 0 (-2cdosxy + 4cdosx2) + -1cos(2x + -1y) * dy = 0 Reorder the terms for easier multiplication: -2cdosxy + 4cdosx2 + -1cos * dy(2x + -1y) = 0 Multiply cos * dy -2cdosxy + 4cdosx2 + -1cdosy(2x + -1y) = 0 -2cdosxy + 4cdosx2 + (2x * -1cdosy + -1y * -1cdosy) = 0 -2cdosxy + 4cdosx2 + (-2cdosxy + 1cdosy2) = 0 Reorder the terms: -2cdosxy + -2cdosxy + 4cdosx2 + 1cdosy2 = 0 Combine like terms: -2cdosxy + -2cdosxy = -4cdosxy -4cdosxy + 4cdosx2 + 1cdosy2 = 0 Solving -4cdosxy + 4cdosx2 + 1cdosy2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'cdos'. cdos(-4xy + 4x2 + y2) = 0 Factor a trinomial. cdos((2x + -1y)(2x + -1y)) = 0Subproblem 1
Set the factor 'cdos' equal to zero and attempt to solve: Simplifying cdos = 0 Solving cdos = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cdos = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 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 c to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + -1y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -1y = 0 + -2x -1y = 0 + -2x Remove the zero: -1y = -2x Add 'y' to each side of the equation. -1y + y = -2x + y Combine like terms: -1y + y = 0 0 = -2x + y Simplifying 0 = -2x + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing c to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + -1y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -1y = 0 + -2x -1y = 0 + -2x Remove the zero: -1y = -2x Add 'y' to each side of the equation. -1y + y = -2x + y Combine like terms: -1y + y = 0 0 = -2x + y Simplifying 0 = -2x + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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