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Simplifying x5 + -9x3 + -8x = 0 Reorder the terms: -8x + -9x3 + x5 = 0 Solving -8x + -9x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + -9x2 + x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-8 + -9x2 + x4)' equal to zero and attempt to solve: Simplifying -8 + -9x2 + x4 = 0 Solving -8 + -9x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -9x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + -9x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9x2 + x4 = 0 + 8 -9x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 -9x2 + x4 = 8 The x term is -9x2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x2 + 20.25 + x4 = 8 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = 8 + 20.25 Combine like terms: 8 + 20.25 = 28.25 20.25 + -9x2 + x4 = 28.25 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x2 + -4.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x2 + -4.5 = 5.315072906 Simplifying x2 + -4.5 = 5.315072906 Reorder the terms: -4.5 + x2 = 5.315072906 Solving -4.5 + x2 = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 5.315072906 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 5.315072906 + 4.5 x2 = 5.315072906 + 4.5 Combine like terms: 5.315072906 + 4.5 = 9.815072906 x2 = 9.815072906 Simplifying x2 = 9.815072906 Take the square root of each side: x = {-3.132901675, 3.132901675}Subproblem 2
x2 + -4.5 = -5.315072906 Simplifying x2 + -4.5 = -5.315072906 Reorder the terms: -4.5 + x2 = -5.315072906 Solving -4.5 + x2 = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -5.315072906 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -5.315072906 + 4.5 x2 = -5.315072906 + 4.5 Combine like terms: -5.315072906 + 4.5 = -0.815072906 x2 = -0.815072906 Simplifying x2 = -0.815072906 Reorder the terms: 0.815072906 + x2 = -0.815072906 + 0.815072906 Combine like terms: -0.815072906 + 0.815072906 = 0.000000000 0.815072906 + x2 = 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. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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