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Simplifying x4 + -18x2 = (x2 + -9)(2x2 + 3) + 23 Reorder the terms: -18x2 + x4 = (x2 + -9)(2x2 + 3) + 23 Reorder the terms: -18x2 + x4 = (-9 + x2)(2x2 + 3) + 23 Reorder the terms: -18x2 + x4 = (-9 + x2)(3 + 2x2) + 23 Multiply (-9 + x2) * (3 + 2x2) -18x2 + x4 = (-9(3 + 2x2) + x2(3 + 2x2)) + 23 -18x2 + x4 = ((3 * -9 + 2x2 * -9) + x2(3 + 2x2)) + 23 -18x2 + x4 = ((-27 + -18x2) + x2(3 + 2x2)) + 23 -18x2 + x4 = (-27 + -18x2 + (3 * x2 + 2x2 * x2)) + 23 -18x2 + x4 = (-27 + -18x2 + (3x2 + 2x4)) + 23 Combine like terms: -18x2 + 3x2 = -15x2 -18x2 + x4 = (-27 + -15x2 + 2x4) + 23 Reorder the terms: -18x2 + x4 = -27 + 23 + -15x2 + 2x4 Combine like terms: -27 + 23 = -4 -18x2 + x4 = -4 + -15x2 + 2x4 Solving -18x2 + x4 = -4 + -15x2 + 2x4 Solving for variable 'x'. Reorder the terms: 4 + -18x2 + 15x2 + x4 + -2x4 = -4 + -15x2 + 2x4 + 4 + 15x2 + -2x4 Combine like terms: -18x2 + 15x2 = -3x2 4 + -3x2 + x4 + -2x4 = -4 + -15x2 + 2x4 + 4 + 15x2 + -2x4 Combine like terms: x4 + -2x4 = -1x4 4 + -3x2 + -1x4 = -4 + -15x2 + 2x4 + 4 + 15x2 + -2x4 Reorder the terms: 4 + -3x2 + -1x4 = -4 + 4 + -15x2 + 15x2 + 2x4 + -2x4 Combine like terms: -4 + 4 = 0 4 + -3x2 + -1x4 = 0 + -15x2 + 15x2 + 2x4 + -2x4 4 + -3x2 + -1x4 = -15x2 + 15x2 + 2x4 + -2x4 Combine like terms: -15x2 + 15x2 = 0 4 + -3x2 + -1x4 = 0 + 2x4 + -2x4 4 + -3x2 + -1x4 = 2x4 + -2x4 Combine like terms: 2x4 + -2x4 = 0 4 + -3x2 + -1x4 = 0 Factor a trinomial. (1 + -1x2)(4 + x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(4 + x2) = 0Subproblem 1
Set the factor '(4 + x2)' equal to zero and attempt to solve: Simplifying 4 + x2 = 0 Solving 4 + x2 = 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 + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 0 + -4 x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x2 = -4 Simplifying x2 = -4 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 = 1Solution
x = {-1, 1}
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