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