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Simplifying 6X3 + 27X2 + 66X = 0 Reorder the terms: 66X + 27X2 + 6X3 = 0 Solving 66X + 27X2 + 6X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '3X'. 3X(22 + 9X + 2X2) = 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 '(22 + 9X + 2X2)' equal to zero and attempt to solve: Simplifying 22 + 9X + 2X2 = 0 Solving 22 + 9X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11 + 4.5X + X2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + 4.5X + -11 + X2 = 0 + -11 Reorder the terms: 11 + -11 + 4.5X + X2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 4.5X + X2 = 0 + -11 4.5X + X2 = 0 + -11 Combine like terms: 0 + -11 = -11 4.5X + X2 = -11 The X term is 4.5X. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5X + 5.0625 + X2 = -11 + 5.0625 Reorder the terms: 5.0625 + 4.5X + X2 = -11 + 5.0625 Combine like terms: -11 + 5.0625 = -5.9375 5.0625 + 4.5X + X2 = -5.9375 Factor a perfect square on the left side: (X + 2.25)(X + 2.25) = -5.9375 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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