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Simplifying x5 + 10x3 + 5x = 0 Reorder the terms: 5x + 10x3 + x5 = 0 Solving 5x + 10x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 10x2 + 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 '(5 + 10x2 + x4)' equal to zero and attempt to solve: Simplifying 5 + 10x2 + x4 = 0 Solving 5 + 10x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 10x2 + -5 + x4 = 0 + -5 Reorder the terms: 5 + -5 + 10x2 + x4 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 10x2 + x4 = 0 + -5 10x2 + x4 = 0 + -5 Combine like terms: 0 + -5 = -5 10x2 + x4 = -5 The x term is 10x2. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x2 + 25 + x4 = -5 + 25 Reorder the terms: 25 + 10x2 + x4 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + 10x2 + x4 = 20 Factor a perfect square on the left side: (x2 + 5)(x2 + 5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x2 + 5) equal to 4.472135955 and -4.472135955.Subproblem 1
x2 + 5 = 4.472135955 Simplifying x2 + 5 = 4.472135955 Reorder the terms: 5 + x2 = 4.472135955 Solving 5 + x2 = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = 4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 4.472135955 + -5 x2 = 4.472135955 + -5 Combine like terms: 4.472135955 + -5 = -0.527864045 x2 = -0.527864045 Simplifying x2 = -0.527864045 Reorder the terms: 0.527864045 + x2 = -0.527864045 + 0.527864045 Combine like terms: -0.527864045 + 0.527864045 = 0.000000000 0.527864045 + x2 = 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
x2 + 5 = -4.472135955 Simplifying x2 + 5 = -4.472135955 Reorder the terms: 5 + x2 = -4.472135955 Solving 5 + x2 = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = -4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = -4.472135955 + -5 x2 = -4.472135955 + -5 Combine like terms: -4.472135955 + -5 = -9.472135955 x2 = -9.472135955 Simplifying x2 = -9.472135955 Reorder the terms: 9.472135955 + x2 = -9.472135955 + 9.472135955 Combine like terms: -9.472135955 + 9.472135955 = 0.000000000 9.472135955 + 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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