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Simplifying x8 + -7x4 + 12 = 0 Reorder the terms: 12 + -7x4 + x8 = 0 Solving 12 + -7x4 + x8 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -1x4)(4 + -1x4) = 0 Factor a difference between two squares. (3 + -1x4)((2 + x2)(2 + -1x2)) = 0Subproblem 1
Set the factor '(3 + -1x4)' equal to zero and attempt to solve: Simplifying 3 + -1x4 = 0 Solving 3 + -1x4 = 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 + -1x4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x4 = 0 + -3 -1x4 = 0 + -3 Combine like terms: 0 + -3 = -3 -1x4 = -3 Divide each side by '-1'. x4 = 3 Simplifying x4 = 3 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 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 = {-1.414213562, 1.414213562}
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