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Simplifying x6 + -8x3 + 8 = 0 Reorder the terms: 8 + -8x3 + x6 = 0 Solving 8 + -8x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -8x3 + -8 + x6 = 0 + -8 Reorder the terms: 8 + -8 + -8x3 + x6 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -8x3 + x6 = 0 + -8 -8x3 + x6 = 0 + -8 Combine like terms: 0 + -8 = -8 -8x3 + x6 = -8 The x term is -8x3. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x3 + 16 + x6 = -8 + 16 Reorder the terms: 16 + -8x3 + x6 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + -8x3 + x6 = 8 Factor a perfect square on the left side: (x3 + -4)(x3 + -4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x3 + -4) equal to 2.828427125 and -2.828427125.Subproblem 1
x3 + -4 = 2.828427125 Simplifying x3 + -4 = 2.828427125 Reorder the terms: -4 + x3 = 2.828427125 Solving -4 + x3 = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x3 = 2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + x3 = 2.828427125 + 4 x3 = 2.828427125 + 4 Combine like terms: 2.828427125 + 4 = 6.828427125 x3 = 6.828427125 Simplifying x3 = 6.828427125 Reorder the terms: -6.828427125 + x3 = 6.828427125 + -6.828427125 Combine like terms: 6.828427125 + -6.828427125 = 0.000000000 -6.828427125 + 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 + -4 = -2.828427125 Simplifying x3 + -4 = -2.828427125 Reorder the terms: -4 + x3 = -2.828427125 Solving -4 + x3 = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x3 = -2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + x3 = -2.828427125 + 4 x3 = -2.828427125 + 4 Combine like terms: -2.828427125 + 4 = 1.171572875 x3 = 1.171572875 Simplifying x3 = 1.171572875 Reorder the terms: -1.171572875 + x3 = 1.171572875 + -1.171572875 Combine like terms: 1.171572875 + -1.171572875 = 0.000000000 -1.171572875 + 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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