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Simplifying x6 + 8x3 + -6 = 0 Reorder the terms: -6 + 8x3 + x6 = 0 Solving -6 + 8x3 + x6 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 8x3 + 6 + x6 = 0 + 6 Reorder the terms: -6 + 6 + 8x3 + x6 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 8x3 + x6 = 0 + 6 8x3 + x6 = 0 + 6 Combine like terms: 0 + 6 = 6 8x3 + x6 = 6 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 = 6 + 16 Reorder the terms: 16 + 8x3 + x6 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + 8x3 + x6 = 22 Factor a perfect square on the left side: (x3 + 4)(x3 + 4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x3 + 4) equal to 4.69041576 and -4.69041576.Subproblem 1
x3 + 4 = 4.69041576 Simplifying x3 + 4 = 4.69041576 Reorder the terms: 4 + x3 = 4.69041576 Solving 4 + x3 = 4.69041576 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 = 4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + x3 = 4.69041576 + -4 x3 = 4.69041576 + -4 Combine like terms: 4.69041576 + -4 = 0.69041576 x3 = 0.69041576 Simplifying x3 = 0.69041576 Reorder the terms: -0.69041576 + x3 = 0.69041576 + -0.69041576 Combine like terms: 0.69041576 + -0.69041576 = 0.00000000 -0.69041576 + 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 + 4 = -4.69041576 Simplifying x3 + 4 = -4.69041576 Reorder the terms: 4 + x3 = -4.69041576 Solving 4 + x3 = -4.69041576 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 = -4.69041576 + -4 Combine like terms: 4 + -4 = 0 0 + x3 = -4.69041576 + -4 x3 = -4.69041576 + -4 Combine like terms: -4.69041576 + -4 = -8.69041576 x3 = -8.69041576 Simplifying x3 = -8.69041576 Reorder the terms: 8.69041576 + x3 = -8.69041576 + 8.69041576 Combine like terms: -8.69041576 + 8.69041576 = 0.00000000 8.69041576 + 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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