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Simplifying x6 + -9x4 + -1x2 = 0 Reorder the terms: -1x2 + -9x4 + x6 = 0 Solving -1x2 + -9x4 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + -9x2 + x4) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-1 + -9x2 + x4)' equal to zero and attempt to solve: Simplifying -1 + -9x2 + x4 = 0 Solving -1 + -9x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -9x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + -9x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -9x2 + x4 = 0 + 1 -9x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 -9x2 + x4 = 1 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 = 1 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = 1 + 20.25 Combine like terms: 1 + 20.25 = 21.25 20.25 + -9x2 + x4 = 21.25 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x2 + -4.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x2 + -4.5 = 4.609772229 Simplifying x2 + -4.5 = 4.609772229 Reorder the terms: -4.5 + x2 = 4.609772229 Solving -4.5 + x2 = 4.609772229 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 = 4.609772229 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 4.609772229 + 4.5 x2 = 4.609772229 + 4.5 Combine like terms: 4.609772229 + 4.5 = 9.109772229 x2 = 9.109772229 Simplifying x2 = 9.109772229 Take the square root of each side: x = {-3.018239922, 3.018239922}Subproblem 2
x2 + -4.5 = -4.609772229 Simplifying x2 + -4.5 = -4.609772229 Reorder the terms: -4.5 + x2 = -4.609772229 Solving -4.5 + x2 = -4.609772229 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 = -4.609772229 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -4.609772229 + 4.5 x2 = -4.609772229 + 4.5 Combine like terms: -4.609772229 + 4.5 = -0.109772229 x2 = -0.109772229 Simplifying x2 = -0.109772229 Reorder the terms: 0.109772229 + x2 = -0.109772229 + 0.109772229 Combine like terms: -0.109772229 + 0.109772229 = 0.000000000 0.109772229 + 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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