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Simplifying 0 = 3x3 + 9x2 + -27x Reorder the terms: 0 = -27x + 9x2 + 3x3 Solving 0 = -27x + 9x2 + 3x3 Solving for variable 'x'. Remove the zero: 27x + -9x2 + -3x3 = -27x + 9x2 + 3x3 + 27x + -9x2 + -3x3 Reorder the terms: 27x + -9x2 + -3x3 = -27x + 27x + 9x2 + -9x2 + 3x3 + -3x3 Combine like terms: -27x + 27x = 0 27x + -9x2 + -3x3 = 0 + 9x2 + -9x2 + 3x3 + -3x3 27x + -9x2 + -3x3 = 9x2 + -9x2 + 3x3 + -3x3 Combine like terms: 9x2 + -9x2 = 0 27x + -9x2 + -3x3 = 0 + 3x3 + -3x3 27x + -9x2 + -3x3 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 27x + -9x2 + -3x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(9 + -3x + -1x2) = 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 '(9 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 9 + -3x + -1x2 = 0 Solving 9 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 3x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 3x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 3x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3x + x2 = 0 + 9 3x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 3x + x2 = 9 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 9 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 9 + 2.25 Combine like terms: 9 + 2.25 = 11.25 2.25 + 3x + x2 = 11.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 1.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 1.5 = 3.354101966 Simplifying x + 1.5 = 3.354101966 Reorder the terms: 1.5 + x = 3.354101966 Solving 1.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.354101966 + -1.5 x = 3.354101966 + -1.5 Combine like terms: 3.354101966 + -1.5 = 1.854101966 x = 1.854101966 Simplifying x = 1.854101966Subproblem 2
x + 1.5 = -3.354101966 Simplifying x + 1.5 = -3.354101966 Reorder the terms: 1.5 + x = -3.354101966 Solving 1.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.354101966 + -1.5 x = -3.354101966 + -1.5 Combine like terms: -3.354101966 + -1.5 = -4.854101966 x = -4.854101966 Simplifying x = -4.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.854101966, -4.854101966}Solution
x = {0, 1.854101966, -4.854101966}
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