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Simplifying 0 = x8 + -5x4 + 4 Reorder the terms: 0 = 4 + -5x4 + x8 Solving 0 = 4 + -5x4 + x8 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + 5x4 + -1x8 = 4 + -5x4 + x8 + -4 + 5x4 + -1x8 Reorder the terms: -4 + 5x4 + -1x8 = 4 + -4 + -5x4 + 5x4 + x8 + -1x8 Combine like terms: 4 + -4 = 0 -4 + 5x4 + -1x8 = 0 + -5x4 + 5x4 + x8 + -1x8 -4 + 5x4 + -1x8 = -5x4 + 5x4 + x8 + -1x8 Combine like terms: -5x4 + 5x4 = 0 -4 + 5x4 + -1x8 = 0 + x8 + -1x8 -4 + 5x4 + -1x8 = x8 + -1x8 Combine like terms: x8 + -1x8 = 0 -4 + 5x4 + -1x8 = 0 Factor a trinomial. (-4 + x4)(1 + -1x4) = 0 Factor a difference between two squares. ((2 + x2)(-2 + x2))(1 + -1x4) = 0 Factor a difference between two squares. ((1 + x2)(1 + -1x2))(2 + x2)(-2 + x2) = 0 Factor a difference between two squares. ((1 + x2)((1 + x)(1 + -1x)))(2 + x2)(-2 + x2) = 0Subproblem 1
Set the factor '(2 + x2)' equal to zero and attempt to solve: Simplifying 2 + x2 = 0 Solving 2 + x2 = 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 + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 0 + -2 x2 = 0 + -2 Combine like terms: 0 + -2 = -2 x2 = -2 Simplifying x2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-2 + x2)' equal to zero and attempt to solve: Simplifying -2 + x2 = 0 Solving -2 + x2 = 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 + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 0 + 2 x2 = 0 + 2 Combine like terms: 0 + 2 = 2 x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}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.Subproblem 4
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 5
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-1.414213562, 1.414213562, -1, 1}
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