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Simplifying -9 + 9X + -2X2 = X3 + -4X2 + X + -9 Reorder the terms: -9 + 9X + -2X2 = -9 + X + -4X2 + X3 Add '9' to each side of the equation. -9 + 9X + 9 + -2X2 = -9 + X + -4X2 + 9 + X3 Reorder the terms: -9 + 9 + 9X + -2X2 = -9 + X + -4X2 + 9 + X3 Combine like terms: -9 + 9 = 0 0 + 9X + -2X2 = -9 + X + -4X2 + 9 + X3 9X + -2X2 = -9 + X + -4X2 + 9 + X3 Reorder the terms: 9X + -2X2 = -9 + 9 + X + -4X2 + X3 Combine like terms: -9 + 9 = 0 9X + -2X2 = 0 + X + -4X2 + X3 9X + -2X2 = X + -4X2 + X3 Solving 9X + -2X2 = X + -4X2 + X3 Solving for variable 'X'. Reorder the terms: 9X + -1X + -2X2 + 4X2 + -1X3 = X + -4X2 + X3 + -1X + 4X2 + -1X3 Combine like terms: 9X + -1X = 8X 8X + -2X2 + 4X2 + -1X3 = X + -4X2 + X3 + -1X + 4X2 + -1X3 Combine like terms: -2X2 + 4X2 = 2X2 8X + 2X2 + -1X3 = X + -4X2 + X3 + -1X + 4X2 + -1X3 Reorder the terms: 8X + 2X2 + -1X3 = X + -1X + -4X2 + 4X2 + X3 + -1X3 Combine like terms: X + -1X = 0 8X + 2X2 + -1X3 = 0 + -4X2 + 4X2 + X3 + -1X3 8X + 2X2 + -1X3 = -4X2 + 4X2 + X3 + -1X3 Combine like terms: -4X2 + 4X2 = 0 8X + 2X2 + -1X3 = 0 + X3 + -1X3 8X + 2X2 + -1X3 = X3 + -1X3 Combine like terms: X3 + -1X3 = 0 8X + 2X2 + -1X3 = 0 Factor out the Greatest Common Factor (GCF), 'X'. X(8 + 2X + -1X2) = 0 Factor a trinomial. X((4 + -1X)(2 + X)) = 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 '(4 + -1X)' equal to zero and attempt to solve: Simplifying 4 + -1X = 0 Solving 4 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1X = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1X = 0 + -4 -1X = 0 + -4 Combine like terms: 0 + -4 = -4 -1X = -4 Divide each side by '-1'. X = 4 Simplifying X = 4Subproblem 3
Set the factor '(2 + X)' equal to zero and attempt to solve: Simplifying 2 + X = 0 Solving 2 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 0 + -2 Combine like terms: 2 + -2 = 0 0 + X = 0 + -2 X = 0 + -2 Combine like terms: 0 + -2 = -2 X = -2 Simplifying X = -2Solution
X = {0, 4, -2}
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