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Simplifying (2x4 + -6x2 + 8) + (-1x4 + 3x2 + -12) = 0 Reorder the terms: (8 + -6x2 + 2x4) + (-1x4 + 3x2 + -12) = 0 Remove parenthesis around (8 + -6x2 + 2x4) 8 + -6x2 + 2x4 + (-1x4 + 3x2 + -12) = 0 Reorder the terms: 8 + -6x2 + 2x4 + (-12 + 3x2 + -1x4) = 0 Remove parenthesis around (-12 + 3x2 + -1x4) 8 + -6x2 + 2x4 + -12 + 3x2 + -1x4 = 0 Reorder the terms: 8 + -12 + -6x2 + 3x2 + 2x4 + -1x4 = 0 Combine like terms: 8 + -12 = -4 -4 + -6x2 + 3x2 + 2x4 + -1x4 = 0 Combine like terms: -6x2 + 3x2 = -3x2 -4 + -3x2 + 2x4 + -1x4 = 0 Combine like terms: 2x4 + -1x4 = 1x4 -4 + -3x2 + 1x4 = 0 Solving -4 + -3x2 + 1x4 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. (-1 + -1x2)((2 + x)(2 + -1x)) = 0Subproblem 1
Set the factor '(-1 + -1x2)' equal to zero and attempt to solve: Simplifying -1 + -1x2 = 0 Solving -1 + -1x2 = 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 + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x2 = 0 + 1 -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1x2 = 1 Divide each side by '-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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-2, 2}
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