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Simplifying 27x6 + -81x3 + 8 = 0 Reorder the terms: 8 + -81x3 + 27x6 = 0 Solving 8 + -81x3 + 27x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.2962962963 + -3x3 + x6 = 0 Move the constant term to the right: Add '-0.2962962963' to each side of the equation. 0.2962962963 + -3x3 + -0.2962962963 + x6 = 0 + -0.2962962963 Reorder the terms: 0.2962962963 + -0.2962962963 + -3x3 + x6 = 0 + -0.2962962963 Combine like terms: 0.2962962963 + -0.2962962963 = 0.0000000000 0.0000000000 + -3x3 + x6 = 0 + -0.2962962963 -3x3 + x6 = 0 + -0.2962962963 Combine like terms: 0 + -0.2962962963 = -0.2962962963 -3x3 + x6 = -0.2962962963 The x term is -3x3. 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. -3x3 + 2.25 + x6 = -0.2962962963 + 2.25 Reorder the terms: 2.25 + -3x3 + x6 = -0.2962962963 + 2.25 Combine like terms: -0.2962962963 + 2.25 = 1.9537037037 2.25 + -3x3 + x6 = 1.9537037037 Factor a perfect square on the left side: (x3 + -1.5)(x3 + -1.5) = 1.9537037037 Calculate the square root of the right side: 1.397749514 Break this problem into two subproblems by setting (x3 + -1.5) equal to 1.397749514 and -1.397749514.Subproblem 1
x3 + -1.5 = 1.397749514 Simplifying x3 + -1.5 = 1.397749514 Reorder the terms: -1.5 + x3 = 1.397749514 Solving -1.5 + x3 = 1.397749514 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 + x3 = 1.397749514 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x3 = 1.397749514 + 1.5 x3 = 1.397749514 + 1.5 Combine like terms: 1.397749514 + 1.5 = 2.897749514 x3 = 2.897749514 Simplifying x3 = 2.897749514 Reorder the terms: -2.897749514 + x3 = 2.897749514 + -2.897749514 Combine like terms: 2.897749514 + -2.897749514 = 0.000000000 -2.897749514 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + -1.5 = -1.397749514 Simplifying x3 + -1.5 = -1.397749514 Reorder the terms: -1.5 + x3 = -1.397749514 Solving -1.5 + x3 = -1.397749514 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 + x3 = -1.397749514 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x3 = -1.397749514 + 1.5 x3 = -1.397749514 + 1.5 Combine like terms: -1.397749514 + 1.5 = 0.102250486 x3 = 0.102250486 Simplifying x3 = 0.102250486 Reorder the terms: -0.102250486 + x3 = 0.102250486 + -0.102250486 Combine like terms: 0.102250486 + -0.102250486 = 0.000000000 -0.102250486 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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