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Simplifying x6 + 2x4 + -81x2 = 0 Reorder the terms: -81x2 + 2x4 + x6 = 0 Solving -81x2 + 2x4 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-81 + 2x2 + 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 '(-81 + 2x2 + x4)' equal to zero and attempt to solve: Simplifying -81 + 2x2 + x4 = 0 Solving -81 + 2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 2x2 + 81 + x4 = 0 + 81 Reorder the terms: -81 + 81 + 2x2 + x4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 2x2 + x4 = 0 + 81 2x2 + x4 = 0 + 81 Combine like terms: 0 + 81 = 81 2x2 + x4 = 81 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 81 + 1 Reorder the terms: 1 + 2x2 + x4 = 81 + 1 Combine like terms: 81 + 1 = 82 1 + 2x2 + x4 = 82 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x2 + 1) equal to 9.055385138 and -9.055385138.Subproblem 1
x2 + 1 = 9.055385138 Simplifying x2 + 1 = 9.055385138 Reorder the terms: 1 + x2 = 9.055385138 Solving 1 + x2 = 9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 9.055385138 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 9.055385138 + -1 x2 = 9.055385138 + -1 Combine like terms: 9.055385138 + -1 = 8.055385138 x2 = 8.055385138 Simplifying x2 = 8.055385138 Take the square root of each side: x = {-2.838201039, 2.838201039}Subproblem 2
x2 + 1 = -9.055385138 Simplifying x2 + 1 = -9.055385138 Reorder the terms: 1 + x2 = -9.055385138 Solving 1 + x2 = -9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -9.055385138 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -9.055385138 + -1 x2 = -9.055385138 + -1 Combine like terms: -9.055385138 + -1 = -10.055385138 x2 = -10.055385138 Simplifying x2 = -10.055385138 Reorder the terms: 10.055385138 + x2 = -10.055385138 + 10.055385138 Combine like terms: -10.055385138 + 10.055385138 = 0.000000000 10.055385138 + 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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