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Simplifying x6 + -54x3 + -27 = 0 Reorder the terms: -27 + -54x3 + x6 = 0 Solving -27 + -54x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -54x3 + 27 + x6 = 0 + 27 Reorder the terms: -27 + 27 + -54x3 + x6 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -54x3 + x6 = 0 + 27 -54x3 + x6 = 0 + 27 Combine like terms: 0 + 27 = 27 -54x3 + x6 = 27 The x term is -54x3. Take half its coefficient (-27). Square it (729) and add it to both sides. Add '729' to each side of the equation. -54x3 + 729 + x6 = 27 + 729 Reorder the terms: 729 + -54x3 + x6 = 27 + 729 Combine like terms: 27 + 729 = 756 729 + -54x3 + x6 = 756 Factor a perfect square on the left side: (x3 + -27)(x3 + -27) = 756 Calculate the square root of the right side: 27.49545417 Break this problem into two subproblems by setting (x3 + -27) equal to 27.49545417 and -27.49545417.Subproblem 1
x3 + -27 = 27.49545417 Simplifying x3 + -27 = 27.49545417 Reorder the terms: -27 + x3 = 27.49545417 Solving -27 + x3 = 27.49545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x3 = 27.49545417 + 27 Combine like terms: -27 + 27 = 0 0 + x3 = 27.49545417 + 27 x3 = 27.49545417 + 27 Combine like terms: 27.49545417 + 27 = 54.49545417 x3 = 54.49545417 Simplifying x3 = 54.49545417 Reorder the terms: -54.49545417 + x3 = 54.49545417 + -54.49545417 Combine like terms: 54.49545417 + -54.49545417 = 0.00000000 -54.49545417 + x3 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + -27 = -27.49545417 Simplifying x3 + -27 = -27.49545417 Reorder the terms: -27 + x3 = -27.49545417 Solving -27 + x3 = -27.49545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + x3 = -27.49545417 + 27 Combine like terms: -27 + 27 = 0 0 + x3 = -27.49545417 + 27 x3 = -27.49545417 + 27 Combine like terms: -27.49545417 + 27 = -0.49545417 x3 = -0.49545417 Simplifying x3 = -0.49545417 Reorder the terms: 0.49545417 + x3 = -0.49545417 + 0.49545417 Combine like terms: -0.49545417 + 0.49545417 = 0.00000000 0.49545417 + x3 = 0.00000000 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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