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Simplifying x5 + 3x3 + -6x = 0 Reorder the terms: -6x + 3x3 + x5 = 0 Solving -6x + 3x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 3x2 + 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 '(-6 + 3x2 + x4)' equal to zero and attempt to solve: Simplifying -6 + 3x2 + x4 = 0 Solving -6 + 3x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 3x2 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + 3x2 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3x2 + x4 = 0 + 6 3x2 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 3x2 + x4 = 6 The x term is 3x2. 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. 3x2 + 2.25 + x4 = 6 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + 3x2 + x4 = 8.25 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x2 + 1.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x2 + 1.5 = 2.872281323 Simplifying x2 + 1.5 = 2.872281323 Reorder the terms: 1.5 + x2 = 2.872281323 Solving 1.5 + x2 = 2.872281323 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 + x2 = 2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 2.872281323 + -1.5 x2 = 2.872281323 + -1.5 Combine like terms: 2.872281323 + -1.5 = 1.372281323 x2 = 1.372281323 Simplifying x2 = 1.372281323 Take the square root of each side: x = {-1.171444119, 1.171444119}Subproblem 2
x2 + 1.5 = -2.872281323 Simplifying x2 + 1.5 = -2.872281323 Reorder the terms: 1.5 + x2 = -2.872281323 Solving 1.5 + x2 = -2.872281323 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 + x2 = -2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -2.872281323 + -1.5 x2 = -2.872281323 + -1.5 Combine like terms: -2.872281323 + -1.5 = -4.372281323 x2 = -4.372281323 Simplifying x2 = -4.372281323 Reorder the terms: 4.372281323 + x2 = -4.372281323 + 4.372281323 Combine like terms: -4.372281323 + 4.372281323 = 0.000000000 4.372281323 + 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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