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Simplifying 0 = x4 + -4x2 + -45 Reorder the terms: 0 = -45 + -4x2 + x4 Solving 0 = -45 + -4x2 + x4 Solving for variable 'x'. Combine like terms: 0 + 45 = 45 45 + 4x2 + -1x4 = -45 + -4x2 + x4 + 45 + 4x2 + -1x4 Reorder the terms: 45 + 4x2 + -1x4 = -45 + 45 + -4x2 + 4x2 + x4 + -1x4 Combine like terms: -45 + 45 = 0 45 + 4x2 + -1x4 = 0 + -4x2 + 4x2 + x4 + -1x4 45 + 4x2 + -1x4 = -4x2 + 4x2 + x4 + -1x4 Combine like terms: -4x2 + 4x2 = 0 45 + 4x2 + -1x4 = 0 + x4 + -1x4 45 + 4x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 45 + 4x2 + -1x4 = 0 Factor a trinomial. (9 + -1x2)(5 + x2) = 0 Factor a difference between two squares. ((3 + x)(3 + -1x))(5 + x2) = 0Subproblem 1
Set the factor '(5 + x2)' equal to zero and attempt to solve: Simplifying 5 + x2 = 0 Solving 5 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 0 + -5 x2 = 0 + -5 Combine like terms: 0 + -5 = -5 x2 = -5 Simplifying x2 = -5 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-3, 3}
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