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Simplifying x5 + 6x3 + 7x = 0 Reorder the terms: 7x + 6x3 + x5 = 0 Solving 7x + 6x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(7 + 6x2 + 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 '(7 + 6x2 + x4)' equal to zero and attempt to solve: Simplifying 7 + 6x2 + x4 = 0 Solving 7 + 6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6x2 + -7 + x4 = 0 + -7 Reorder the terms: 7 + -7 + 6x2 + x4 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x2 + x4 = 0 + -7 6x2 + x4 = 0 + -7 Combine like terms: 0 + -7 = -7 6x2 + x4 = -7 The x term is 6x2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x2 + 9 + x4 = -7 + 9 Reorder the terms: 9 + 6x2 + x4 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + 6x2 + x4 = 2 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x2 + 3) equal to 1.414213562 and -1.414213562.Subproblem 1
x2 + 3 = 1.414213562 Simplifying x2 + 3 = 1.414213562 Reorder the terms: 3 + x2 = 1.414213562 Solving 3 + x2 = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 1.414213562 + -3 x2 = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 x2 = -1.585786438 Simplifying x2 = -1.585786438 Reorder the terms: 1.585786438 + x2 = -1.585786438 + 1.585786438 Combine like terms: -1.585786438 + 1.585786438 = 0.000000000 1.585786438 + 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 + 3 = -1.414213562 Simplifying x2 + 3 = -1.414213562 Reorder the terms: 3 + x2 = -1.414213562 Solving 3 + x2 = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -1.414213562 + -3 x2 = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 x2 = -4.414213562 Simplifying x2 = -4.414213562 Reorder the terms: 4.414213562 + x2 = -4.414213562 + 4.414213562 Combine like terms: -4.414213562 + 4.414213562 = 0.000000000 4.414213562 + 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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