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Simplifying 27x6 + 2x3 + -5 = 0 Reorder the terms: -5 + 2x3 + 27x6 = 0 Solving -5 + 2x3 + 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'. -0.1851851852 + 0.07407407407x3 + x6 = 0 Move the constant term to the right: Add '0.1851851852' to each side of the equation. -0.1851851852 + 0.07407407407x3 + 0.1851851852 + x6 = 0 + 0.1851851852 Reorder the terms: -0.1851851852 + 0.1851851852 + 0.07407407407x3 + x6 = 0 + 0.1851851852 Combine like terms: -0.1851851852 + 0.1851851852 = 0.0000000000 0.0000000000 + 0.07407407407x3 + x6 = 0 + 0.1851851852 0.07407407407x3 + x6 = 0 + 0.1851851852 Combine like terms: 0 + 0.1851851852 = 0.1851851852 0.07407407407x3 + x6 = 0.1851851852 The x term is 0.07407407407x3. Take half its coefficient (0.03703703704). Square it (0.001371742113) and add it to both sides. Add '0.001371742113' to each side of the equation. 0.07407407407x3 + 0.001371742113 + x6 = 0.1851851852 + 0.001371742113 Reorder the terms: 0.001371742113 + 0.07407407407x3 + x6 = 0.1851851852 + 0.001371742113 Combine like terms: 0.1851851852 + 0.001371742113 = 0.186556927313 0.001371742113 + 0.07407407407x3 + x6 = 0.186556927313 Factor a perfect square on the left side: (x3 + 0.03703703704)(x3 + 0.03703703704) = 0.186556927313 Calculate the square root of the right side: 0.431922363 Break this problem into two subproblems by setting (x3 + 0.03703703704) equal to 0.431922363 and -0.431922363.Subproblem 1
x3 + 0.03703703704 = 0.431922363 Simplifying x3 + 0.03703703704 = 0.431922363 Reorder the terms: 0.03703703704 + x3 = 0.431922363 Solving 0.03703703704 + x3 = 0.431922363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03703703704' to each side of the equation. 0.03703703704 + -0.03703703704 + x3 = 0.431922363 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + x3 = 0.431922363 + -0.03703703704 x3 = 0.431922363 + -0.03703703704 Combine like terms: 0.431922363 + -0.03703703704 = 0.39488532596 x3 = 0.39488532596 Simplifying x3 = 0.39488532596 Reorder the terms: -0.39488532596 + x3 = 0.39488532596 + -0.39488532596 Combine like terms: 0.39488532596 + -0.39488532596 = 0.00000000000 -0.39488532596 + x3 = 0.00000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 0.03703703704 = -0.431922363 Simplifying x3 + 0.03703703704 = -0.431922363 Reorder the terms: 0.03703703704 + x3 = -0.431922363 Solving 0.03703703704 + x3 = -0.431922363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03703703704' to each side of the equation. 0.03703703704 + -0.03703703704 + x3 = -0.431922363 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + x3 = -0.431922363 + -0.03703703704 x3 = -0.431922363 + -0.03703703704 Combine like terms: -0.431922363 + -0.03703703704 = -0.46895940004 x3 = -0.46895940004 Simplifying x3 = -0.46895940004 Reorder the terms: 0.46895940004 + x3 = -0.46895940004 + 0.46895940004 Combine like terms: -0.46895940004 + 0.46895940004 = 0.00000000000 0.46895940004 + x3 = 0.00000000000 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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