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Simplifying x6 + 29x4 + 125x2 = 0 Reorder the terms: 125x2 + 29x4 + x6 = 0 Solving 125x2 + 29x4 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(125 + 29x2 + 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 '(125 + 29x2 + x4)' equal to zero and attempt to solve: Simplifying 125 + 29x2 + x4 = 0 Solving 125 + 29x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-125' to each side of the equation. 125 + 29x2 + -125 + x4 = 0 + -125 Reorder the terms: 125 + -125 + 29x2 + x4 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + 29x2 + x4 = 0 + -125 29x2 + x4 = 0 + -125 Combine like terms: 0 + -125 = -125 29x2 + x4 = -125 The x term is 29x2. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x2 + 210.25 + x4 = -125 + 210.25 Reorder the terms: 210.25 + 29x2 + x4 = -125 + 210.25 Combine like terms: -125 + 210.25 = 85.25 210.25 + 29x2 + x4 = 85.25 Factor a perfect square on the left side: (x2 + 14.5)(x2 + 14.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x2 + 14.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x2 + 14.5 = 9.233092656 Simplifying x2 + 14.5 = 9.233092656 Reorder the terms: 14.5 + x2 = 9.233092656 Solving 14.5 + x2 = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x2 = 9.233092656 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x2 = 9.233092656 + -14.5 x2 = 9.233092656 + -14.5 Combine like terms: 9.233092656 + -14.5 = -5.266907344 x2 = -5.266907344 Simplifying x2 = -5.266907344 Reorder the terms: 5.266907344 + x2 = -5.266907344 + 5.266907344 Combine like terms: -5.266907344 + 5.266907344 = 0.000000000 5.266907344 + 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 + 14.5 = -9.233092656 Simplifying x2 + 14.5 = -9.233092656 Reorder the terms: 14.5 + x2 = -9.233092656 Solving 14.5 + x2 = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x2 = -9.233092656 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x2 = -9.233092656 + -14.5 x2 = -9.233092656 + -14.5 Combine like terms: -9.233092656 + -14.5 = -23.733092656 x2 = -23.733092656 Simplifying x2 = -23.733092656 Reorder the terms: 23.733092656 + x2 = -23.733092656 + 23.733092656 Combine like terms: -23.733092656 + 23.733092656 = 0.000000000 23.733092656 + 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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