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Simplifying x6 + -4x3 + 1 = 0 Reorder the terms: 1 + -4x3 + x6 = 0 Solving 1 + -4x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4x3 + -1 + x6 = 0 + -1 Reorder the terms: 1 + -1 + -4x3 + x6 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x3 + x6 = 0 + -1 -4x3 + x6 = 0 + -1 Combine like terms: 0 + -1 = -1 -4x3 + x6 = -1 The x term is -4x3. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x3 + 4 + x6 = -1 + 4 Reorder the terms: 4 + -4x3 + x6 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4x3 + x6 = 3 Factor a perfect square on the left side: (x3 + -2)(x3 + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x3 + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
x3 + -2 = 1.732050808 Simplifying x3 + -2 = 1.732050808 Reorder the terms: -2 + x3 = 1.732050808 Solving -2 + x3 = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x3 = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x3 = 1.732050808 + 2 x3 = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 x3 = 3.732050808 Simplifying x3 = 3.732050808 Reorder the terms: -3.732050808 + x3 = 3.732050808 + -3.732050808 Combine like terms: 3.732050808 + -3.732050808 = 0.000000000 -3.732050808 + 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 + -2 = -1.732050808 Simplifying x3 + -2 = -1.732050808 Reorder the terms: -2 + x3 = -1.732050808 Solving -2 + x3 = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x3 = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + x3 = -1.732050808 + 2 x3 = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 x3 = 0.267949192 Simplifying x3 = 0.267949192 Reorder the terms: -0.267949192 + x3 = 0.267949192 + -0.267949192 Combine like terms: 0.267949192 + -0.267949192 = 0.000000000 -0.267949192 + 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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