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Simplifying x6 + 24x4 + 4x2 = 0 Reorder the terms: 4x2 + 24x4 + x6 = 0 Solving 4x2 + 24x4 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(4 + 24x2 + 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 '(4 + 24x2 + x4)' equal to zero and attempt to solve: Simplifying 4 + 24x2 + x4 = 0 Solving 4 + 24x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 24x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + 24x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 24x2 + x4 = 0 + -4 24x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 24x2 + x4 = -4 The x term is 24x2. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x2 + 144 + x4 = -4 + 144 Reorder the terms: 144 + 24x2 + x4 = -4 + 144 Combine like terms: -4 + 144 = 140 144 + 24x2 + x4 = 140 Factor a perfect square on the left side: (x2 + 12)(x2 + 12) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x2 + 12) equal to 11.832159566 and -11.832159566.Subproblem 1
x2 + 12 = 11.832159566 Simplifying x2 + 12 = 11.832159566 Reorder the terms: 12 + x2 = 11.832159566 Solving 12 + x2 = 11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = 11.832159566 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = 11.832159566 + -12 x2 = 11.832159566 + -12 Combine like terms: 11.832159566 + -12 = -0.167840434 x2 = -0.167840434 Simplifying x2 = -0.167840434 Reorder the terms: 0.167840434 + x2 = -0.167840434 + 0.167840434 Combine like terms: -0.167840434 + 0.167840434 = 0.000000000 0.167840434 + 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 + 12 = -11.832159566 Simplifying x2 + 12 = -11.832159566 Reorder the terms: 12 + x2 = -11.832159566 Solving 12 + x2 = -11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = -11.832159566 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = -11.832159566 + -12 x2 = -11.832159566 + -12 Combine like terms: -11.832159566 + -12 = -23.832159566 x2 = -23.832159566 Simplifying x2 = -23.832159566 Reorder the terms: 23.832159566 + x2 = -23.832159566 + 23.832159566 Combine like terms: -23.832159566 + 23.832159566 = 0.000000000 23.832159566 + 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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