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Simplifying 27x3 + -6x2 + 15x = 0 Reorder the terms: 15x + -6x2 + 27x3 = 0 Solving 15x + -6x2 + 27x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(5 + -2x + 9x2) = 0 Ignore the factor 3.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 '(5 + -2x + 9x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + 9x2 = 0 Solving 5 + -2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -0.2222222222x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -0.2222222222x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -0.2222222222x + x2 = 0 + -0.5555555556 -0.2222222222x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -0.2222222222x + x2 = -0.5555555556 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = -0.5555555556 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = -0.5555555556 + 0.01234567901 Combine like terms: -0.5555555556 + 0.01234567901 = -0.54320987659 0.01234567901 + -0.2222222222x + x2 = -0.54320987659 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = -0.54320987659 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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