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Simplifying X(X2 + -1000) = X(X2 + -2X) Reorder the terms: X(-1000 + X2) = X(X2 + -2X) (-1000 * X + X2 * X) = X(X2 + -2X) (-1000X + X3) = X(X2 + -2X) Reorder the terms: -1000X + X3 = X(-2X + X2) -1000X + X3 = (-2X * X + X2 * X) -1000X + X3 = (-2X2 + X3) Add '-1X3' to each side of the equation. -1000X + X3 + -1X3 = -2X2 + X3 + -1X3 Combine like terms: X3 + -1X3 = 0 -1000X + 0 = -2X2 + X3 + -1X3 -1000X = -2X2 + X3 + -1X3 Combine like terms: X3 + -1X3 = 0 -1000X = -2X2 + 0 -1000X = -2X2 Solving -1000X = -2X2 Solving for variable 'X'. Combine like terms: -2X2 + 2X2 = 0 -1000X + 2X2 = 0 Factor out the Greatest Common Factor (GCF), '2X'. 2X(-500 + X) = 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 '(-500 + X)' equal to zero and attempt to solve: Simplifying -500 + X = 0 Solving -500 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + X = 0 + 500 Combine like terms: -500 + 500 = 0 0 + X = 0 + 500 X = 0 + 500 Combine like terms: 0 + 500 = 500 X = 500 Simplifying X = 500Solution
X = {0, 500}
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