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Simplifying 12x3 + -6x2 + 18x = 0 Reorder the terms: 18x + -6x2 + 12x3 = 0 Solving 18x + -6x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(3 + -1x + 2x2) = 0 Ignore the factor 6.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 '(3 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + -1x + 2x2 = 0 Solving 3 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.5x + x2 = 0 + -1.5 -0.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.5x + x2 = -1.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -1.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -1.5 + 0.0625 Combine like terms: -1.5 + 0.0625 = -1.4375 0.0625 + -0.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -1.4375 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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