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Simplifying x4 + -14x2 = 32 Reorder the terms: -14x2 + x4 = 32 Solving -14x2 + x4 = 32 Solving for variable 'x'. Reorder the terms: -32 + -14x2 + x4 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -14x2 + x4 = 0 Factor a trinomial. (-2 + -1x2)(16 + -1x2) = 0 Factor a difference between two squares. (-2 + -1x2)((4 + x)(4 + -1x)) = 0Subproblem 1
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 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-4, 4}
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