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Simplifying 2x(1 + sqrt(x2 + -1y)) * dx + -1sqrt(x2 + -1y) * dy = 0 2x(1 + (x2 * qrst + -1y * qrst)) * dx + -1sqrt(x2 + -1y) * dy = 0 2x(1 + (qrstx2 + -1qrsty)) * dx + -1sqrt(x2 + -1y) * dy = 0 Reorder the terms for easier multiplication: 2x * dx(1 + qrstx2 + -1qrsty) + -1sqrt(x2 + -1y) * dy = 0 Multiply x * dx 2dx2(1 + qrstx2 + -1qrsty) + -1sqrt(x2 + -1y) * dy = 0 (1 * 2dx2 + qrstx2 * 2dx2 + -1qrsty * 2dx2) + -1sqrt(x2 + -1y) * dy = 0 Reorder the terms: (-2dqrstx2y + 2dqrstx4 + 2dx2) + -1sqrt(x2 + -1y) * dy = 0 (-2dqrstx2y + 2dqrstx4 + 2dx2) + -1sqrt(x2 + -1y) * dy = 0 Reorder the terms for easier multiplication: -2dqrstx2y + 2dqrstx4 + 2dx2 + -1qrst * dy(x2 + -1y) = 0 Multiply qrst * dy -2dqrstx2y + 2dqrstx4 + 2dx2 + -1dqrsty(x2 + -1y) = 0 -2dqrstx2y + 2dqrstx4 + 2dx2 + (x2 * -1dqrsty + -1y * -1dqrsty) = 0 -2dqrstx2y + 2dqrstx4 + 2dx2 + (-1dqrstx2y + 1dqrsty2) = 0 Reorder the terms: -2dqrstx2y + -1dqrstx2y + 2dqrstx4 + 1dqrsty2 + 2dx2 = 0 Combine like terms: -2dqrstx2y + -1dqrstx2y = -3dqrstx2y -3dqrstx2y + 2dqrstx4 + 1dqrsty2 + 2dx2 = 0 Solving -3dqrstx2y + 2dqrstx4 + 1dqrsty2 + 2dx2 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'd'. d(-3qrstx2y + 2qrstx4 + qrsty2 + 2x2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(-3qrstx2y + 2qrstx4 + qrsty2 + 2x2)' equal to zero and attempt to solve: Simplifying -3qrstx2y + 2qrstx4 + qrsty2 + 2x2 = 0 Solving -3qrstx2y + 2qrstx4 + qrsty2 + 2x2 = 0 Move all terms containing d to the left, all other terms to the right. Add '3qrstx2y' to each side of the equation. -3qrstx2y + 2qrstx4 + qrsty2 + 3qrstx2y + 2x2 = 0 + 3qrstx2y Reorder the terms: -3qrstx2y + 3qrstx2y + 2qrstx4 + qrsty2 + 2x2 = 0 + 3qrstx2y Combine like terms: -3qrstx2y + 3qrstx2y = 0 0 + 2qrstx4 + qrsty2 + 2x2 = 0 + 3qrstx2y 2qrstx4 + qrsty2 + 2x2 = 0 + 3qrstx2y Remove the zero: 2qrstx4 + qrsty2 + 2x2 = 3qrstx2y Add '-2qrstx4' to each side of the equation. 2qrstx4 + qrsty2 + -2qrstx4 + 2x2 = 3qrstx2y + -2qrstx4 Reorder the terms: 2qrstx4 + -2qrstx4 + qrsty2 + 2x2 = 3qrstx2y + -2qrstx4 Combine like terms: 2qrstx4 + -2qrstx4 = 0 0 + qrsty2 + 2x2 = 3qrstx2y + -2qrstx4 qrsty2 + 2x2 = 3qrstx2y + -2qrstx4 Add '-1qrsty2' to each side of the equation. qrsty2 + -1qrsty2 + 2x2 = 3qrstx2y + -2qrstx4 + -1qrsty2 Combine like terms: qrsty2 + -1qrsty2 = 0 0 + 2x2 = 3qrstx2y + -2qrstx4 + -1qrsty2 2x2 = 3qrstx2y + -2qrstx4 + -1qrsty2 Add '-2x2' to each side of the equation. 2x2 + -2x2 = 3qrstx2y + -2qrstx4 + -1qrsty2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = 3qrstx2y + -2qrstx4 + -1qrsty2 + -2x2 Simplifying 0 = 3qrstx2y + -2qrstx4 + -1qrsty2 + -2x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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