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Simplifying x6 + 3x3 + -9 = 0 Reorder the terms: -9 + 3x3 + x6 = 0 Solving -9 + 3x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 3x3 + 9 + x6 = 0 + 9 Reorder the terms: -9 + 9 + 3x3 + x6 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3x3 + x6 = 0 + 9 3x3 + x6 = 0 + 9 Combine like terms: 0 + 9 = 9 3x3 + x6 = 9 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 = 9 + 2.25 Reorder the terms: 2.25 + 3x3 + x6 = 9 + 2.25 Combine like terms: 9 + 2.25 = 11.25 2.25 + 3x3 + x6 = 11.25 Factor a perfect square on the left side: (x3 + 1.5)(x3 + 1.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x3 + 1.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x3 + 1.5 = 3.354101966 Simplifying x3 + 1.5 = 3.354101966 Reorder the terms: 1.5 + x3 = 3.354101966 Solving 1.5 + x3 = 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 + x3 = 3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x3 = 3.354101966 + -1.5 x3 = 3.354101966 + -1.5 Combine like terms: 3.354101966 + -1.5 = 1.854101966 x3 = 1.854101966 Simplifying x3 = 1.854101966 Reorder the terms: -1.854101966 + x3 = 1.854101966 + -1.854101966 Combine like terms: 1.854101966 + -1.854101966 = 0.000000000 -1.854101966 + 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 = -3.354101966 Simplifying x3 + 1.5 = -3.354101966 Reorder the terms: 1.5 + x3 = -3.354101966 Solving 1.5 + x3 = -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 + x3 = -3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x3 = -3.354101966 + -1.5 x3 = -3.354101966 + -1.5 Combine like terms: -3.354101966 + -1.5 = -4.854101966 x3 = -4.854101966 Simplifying x3 = -4.854101966 Reorder the terms: 4.854101966 + x3 = -4.854101966 + 4.854101966 Combine like terms: -4.854101966 + 4.854101966 = 0.000000000 4.854101966 + 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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