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Simplifying 18x3 + 24x2 + 32x = 0 Reorder the terms: 32x + 24x2 + 18x3 = 0 Solving 32x + 24x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(16 + 12x + 9x2) = 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 '(16 + 12x + 9x2)' equal to zero and attempt to solve: Simplifying 16 + 12x + 9x2 = 0 Solving 16 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.777777778 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + 1.333333333x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + 1.333333333x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + -1.777777778 1.333333333x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 1.333333333x + x2 = -1.777777778 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -1.777777778 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -1.777777778 + 0.4444444442 Combine like terms: -1.777777778 + 0.4444444442 = -1.3333333338 0.4444444442 + 1.333333333x + x2 = -1.3333333338 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -1.3333333338 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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