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Simplifying x6 + -3x3 + -8 = 0 Reorder the terms: -8 + -3x3 + x6 = 0 Solving -8 + -3x3 + 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 + -3x3 + 8 + x6 = 0 + 8 Reorder the terms: -8 + 8 + -3x3 + x6 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3x3 + x6 = 0 + 8 -3x3 + x6 = 0 + 8 Combine like terms: 0 + 8 = 8 -3x3 + x6 = 8 The x term is -3x3. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x3 + 2.25 + x6 = 8 + 2.25 Reorder the terms: 2.25 + -3x3 + x6 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + -3x3 + x6 = 10.25 Factor a perfect square on the left side: (x3 + -1.5)(x3 + -1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x3 + -1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x3 + -1.5 = 3.201562119 Simplifying x3 + -1.5 = 3.201562119 Reorder the terms: -1.5 + x3 = 3.201562119 Solving -1.5 + x3 = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x3 = 3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x3 = 3.201562119 + 1.5 x3 = 3.201562119 + 1.5 Combine like terms: 3.201562119 + 1.5 = 4.701562119 x3 = 4.701562119 Simplifying x3 = 4.701562119 Reorder the terms: -4.701562119 + x3 = 4.701562119 + -4.701562119 Combine like terms: 4.701562119 + -4.701562119 = 0.000000000 -4.701562119 + 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 = -3.201562119 Simplifying x3 + -1.5 = -3.201562119 Reorder the terms: -1.5 + x3 = -3.201562119 Solving -1.5 + x3 = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x3 = -3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x3 = -3.201562119 + 1.5 x3 = -3.201562119 + 1.5 Combine like terms: -3.201562119 + 1.5 = -1.701562119 x3 = -1.701562119 Simplifying x3 = -1.701562119 Reorder the terms: 1.701562119 + x3 = -1.701562119 + 1.701562119 Combine like terms: -1.701562119 + 1.701562119 = 0.000000000 1.701562119 + 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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