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Simplifying 81x3 + -54x2 + 18x = 0 Reorder the terms: 18x + -54x2 + 81x3 = 0 Solving 18x + -54x2 + 81x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9x'. 9x(2 + -6x + 9x2) = 0 Ignore the factor 9.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 '(2 + -6x + 9x2)' equal to zero and attempt to solve: Simplifying 2 + -6x + 9x2 = 0 Solving 2 + -6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.6666666667x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -0.6666666667x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + -0.2222222222 -0.6666666667x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -0.6666666667x + x2 = -0.2222222222 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -0.2222222222 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -0.2222222222 + 0.1111111112 Combine like terms: -0.2222222222 + 0.1111111112 = -0.111111111 0.1111111112 + -0.6666666667x + x2 = -0.111111111 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -0.111111111 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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