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Simplifying x6 + -2x3 + -27 = 0 Reorder the terms: -27 + -2x3 + x6 = 0 Solving -27 + -2x3 + 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 + -2x3 + 27 + x6 = 0 + 27 Reorder the terms: -27 + 27 + -2x3 + x6 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -2x3 + x6 = 0 + 27 -2x3 + x6 = 0 + 27 Combine like terms: 0 + 27 = 27 -2x3 + x6 = 27 The x term is -2x3. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x3 + 1 + x6 = 27 + 1 Reorder the terms: 1 + -2x3 + x6 = 27 + 1 Combine like terms: 27 + 1 = 28 1 + -2x3 + x6 = 28 Factor a perfect square on the left side: (x3 + -1)(x3 + -1) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x3 + -1) equal to 5.291502622 and -5.291502622.Subproblem 1
x3 + -1 = 5.291502622 Simplifying x3 + -1 = 5.291502622 Reorder the terms: -1 + x3 = 5.291502622 Solving -1 + x3 = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x3 = 5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + x3 = 5.291502622 + 1 x3 = 5.291502622 + 1 Combine like terms: 5.291502622 + 1 = 6.291502622 x3 = 6.291502622 Simplifying x3 = 6.291502622 Reorder the terms: -6.291502622 + x3 = 6.291502622 + -6.291502622 Combine like terms: 6.291502622 + -6.291502622 = 0.000000000 -6.291502622 + 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 = -5.291502622 Simplifying x3 + -1 = -5.291502622 Reorder the terms: -1 + x3 = -5.291502622 Solving -1 + x3 = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x3 = -5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + x3 = -5.291502622 + 1 x3 = -5.291502622 + 1 Combine like terms: -5.291502622 + 1 = -4.291502622 x3 = -4.291502622 Simplifying x3 = -4.291502622 Reorder the terms: 4.291502622 + x3 = -4.291502622 + 4.291502622 Combine like terms: -4.291502622 + 4.291502622 = 0.000000000 4.291502622 + 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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