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Simplifying x8 + -10x4 + 9 = 0 Reorder the terms: 9 + -10x4 + x8 = 0 Solving 9 + -10x4 + x8 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x4)(9 + -1x4) = 0 Factor a difference between two squares. ((1 + x2)(1 + -1x2))(9 + -1x4) = 0 Factor a difference between two squares. ((1 + x2)((1 + x)(1 + -1x)))(9 + -1x4) = 0 Factor a difference between two squares. ((3 + x2)(3 + -1x2))(1 + x2)(1 + x)(1 + -1x) = 0Subproblem 1
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 2
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 3
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 = 1Subproblem 4
Set the factor '(3 + x2)' equal to zero and attempt to solve: Simplifying 3 + x2 = 0 Solving 3 + x2 = 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 + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 0 + -3 x2 = 0 + -3 Combine like terms: 0 + -3 = -3 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 5
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}Solution
x = {-1, 1, -1.732050808, 1.732050808}
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