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Simplifying (x2 + 4)((x + 2)(x + -2)) = 0 Reorder the terms: (4 + x2)((x + 2)(x + -2)) = 0 Reorder the terms: (4 + x2)((2 + x)(x + -2)) = 0 Reorder the terms: (4 + x2)((2 + x)(-2 + x)) = 0 Multiply (2 + x) * (-2 + x) (4 + x2)((2(-2 + x) + x(-2 + x))) = 0 (4 + x2)(((-2 * 2 + x * 2) + x(-2 + x))) = 0 (4 + x2)(((-4 + 2x) + x(-2 + x))) = 0 (4 + x2)((-4 + 2x + (-2 * x + x * x))) = 0 (4 + x2)((-4 + 2x + (-2x + x2))) = 0 Combine like terms: 2x + -2x = 0 (4 + x2)((-4 + 0 + x2)) = 0 (4 + x2)((-4 + x2)) = 0 Multiply (4 + x2) * (-4 + x2) (4(-4 + x2) + x2(-4 + x2)) = 0 ((-4 * 4 + x2 * 4) + x2(-4 + x2)) = 0 ((-16 + 4x2) + x2(-4 + x2)) = 0 (-16 + 4x2 + (-4 * x2 + x2 * x2)) = 0 (-16 + 4x2 + (-4x2 + x4)) = 0 Combine like terms: 4x2 + -4x2 = 0 (-16 + 0 + x4) = 0 (-16 + x4) = 0 Solving -16 + x4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x4 = 0 + 16 x4 = 0 + 16 Combine like terms: 0 + 16 = 16 x4 = 16 Simplifying x4 = 16 Reorder the terms: -16 + x4 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + x4 = 0 Factor a difference between two squares. (4 + x2)(-4 + x2) = 0 Factor a difference between two squares. (4 + x2)((2 + x)(-2 + x)) = 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 '(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 + 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 = 2Solution
x = {-2, 2}
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