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Simplifying 2x3 + 3x2 + 9x = 0 Reorder the terms: 9x + 3x2 + 2x3 = 0 Solving 9x + 3x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(9 + 3x + 2x2) = 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 '(9 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + 3x + 2x2 = 0 Solving 9 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 1.5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 1.5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 1.5x + x2 = 0 + -4.5 1.5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 1.5x + x2 = -4.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -4.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -4.5 + 0.5625 Combine like terms: -4.5 + 0.5625 = -3.9375 0.5625 + 1.5x + x2 = -3.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -3.9375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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