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Simplifying 0 = -1x5 + -1x3 + 6x Reorder the terms: 0 = 6x + -1x3 + -1x5 Solving 0 = 6x + -1x3 + -1x5 Solving for variable 'x'. Remove the zero: -6x + x3 + x5 = 6x + -1x3 + -1x5 + -6x + x3 + x5 Reorder the terms: -6x + x3 + x5 = 6x + -6x + -1x3 + x3 + -1x5 + x5 Combine like terms: 6x + -6x = 0 -6x + x3 + x5 = 0 + -1x3 + x3 + -1x5 + x5 -6x + x3 + x5 = -1x3 + x3 + -1x5 + x5 Combine like terms: -1x3 + x3 = 0 -6x + x3 + x5 = 0 + -1x5 + x5 -6x + x3 + x5 = -1x5 + x5 Combine like terms: -1x5 + x5 = 0 -6x + x3 + x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + x2 + x4) = 0 Factor a trinomial. x((-3 + -1x2)(2 + -1x2)) = 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 '(-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 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Solution
x = {0, -1.414213562, 1.414213562}
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