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