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Simplifying 3x3 + -27x2 + 36x = 0 Reorder the terms: 36x + -27x2 + 3x3 = 0 Solving 36x + -27x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(12 + -9x + x2) = 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 '(12 + -9x + x2)' equal to zero and attempt to solve: Simplifying 12 + -9x + x2 = 0 Solving 12 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -9x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -9x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -9x + x2 = 0 + -12 -9x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -9x + x2 = -12 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -12 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -12 + 20.25 Combine like terms: -12 + 20.25 = 8.25 20.25 + -9x + x2 = 8.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -4.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -4.5 = 2.872281323 Simplifying x + -4.5 = 2.872281323 Reorder the terms: -4.5 + x = 2.872281323 Solving -4.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.872281323 + 4.5 x = 2.872281323 + 4.5 Combine like terms: 2.872281323 + 4.5 = 7.372281323 x = 7.372281323 Simplifying x = 7.372281323Subproblem 2
x + -4.5 = -2.872281323 Simplifying x + -4.5 = -2.872281323 Reorder the terms: -4.5 + x = -2.872281323 Solving -4.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -2.872281323 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.872281323 + 4.5 x = -2.872281323 + 4.5 Combine like terms: -2.872281323 + 4.5 = 1.627718677 x = 1.627718677 Simplifying x = 1.627718677Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.372281323, 1.627718677}Solution
x = {0, 7.372281323, 1.627718677}
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