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Simplifying 0 = 4x3 + 12x2 + 18x Reorder the terms: 0 = 18x + 12x2 + 4x3 Solving 0 = 18x + 12x2 + 4x3 Solving for variable 'x'. Remove the zero: -18x + -12x2 + -4x3 = 18x + 12x2 + 4x3 + -18x + -12x2 + -4x3 Reorder the terms: -18x + -12x2 + -4x3 = 18x + -18x + 12x2 + -12x2 + 4x3 + -4x3 Combine like terms: 18x + -18x = 0 -18x + -12x2 + -4x3 = 0 + 12x2 + -12x2 + 4x3 + -4x3 -18x + -12x2 + -4x3 = 12x2 + -12x2 + 4x3 + -4x3 Combine like terms: 12x2 + -12x2 = 0 -18x + -12x2 + -4x3 = 0 + 4x3 + -4x3 -18x + -12x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -18x + -12x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '-2x'. -2x(9 + 6x + 2x2) = 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 '(9 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + 6x + 2x2 = 0 Solving 9 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 3x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 3x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 3x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 3x + x2 = 0 + -4.5 3x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 3x + x2 = -4.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -4.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -4.5 + 2.25 Combine like terms: -4.5 + 2.25 = -2.25 2.25 + 3x + x2 = -2.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -2.25 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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