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Simplifying 0 = 2x5 + -4x3 + -6x Reorder the terms: 0 = -6x + -4x3 + 2x5 Solving 0 = -6x + -4x3 + 2x5 Solving for variable 'x'. Remove the zero: 6x + 4x3 + -2x5 = -6x + -4x3 + 2x5 + 6x + 4x3 + -2x5 Reorder the terms: 6x + 4x3 + -2x5 = -6x + 6x + -4x3 + 4x3 + 2x5 + -2x5 Combine like terms: -6x + 6x = 0 6x + 4x3 + -2x5 = 0 + -4x3 + 4x3 + 2x5 + -2x5 6x + 4x3 + -2x5 = -4x3 + 4x3 + 2x5 + -2x5 Combine like terms: -4x3 + 4x3 = 0 6x + 4x3 + -2x5 = 0 + 2x5 + -2x5 6x + 4x3 + -2x5 = 2x5 + -2x5 Combine like terms: 2x5 + -2x5 = 0 6x + 4x3 + -2x5 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + 2x2 + -1x4) = 0 Factor a trinomial. 2x((3 + -1x2)(1 + x2)) = 0 Ignore the factor 2.Subproblem 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 '(3 + -1x2)' equal to zero and attempt to solve: Simplifying 3 + -1x2 = 0 Solving 3 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x2 = 0 + -3 -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1x2 = -3 Divide each side by '-1'. x2 = 3 Simplifying x2 = 3 Take the square root of each side: x = {-1.732050808, 1.732050808}Subproblem 3
Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 0 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 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0, -1.732050808, 1.732050808}
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