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Simplifying (2x2 + 8)(4 + -1x2) = 0 Reorder the terms: (8 + 2x2)(4 + -1x2) = 0 Multiply (8 + 2x2) * (4 + -1x2) (8(4 + -1x2) + 2x2 * (4 + -1x2)) = 0 ((4 * 8 + -1x2 * 8) + 2x2 * (4 + -1x2)) = 0 ((32 + -8x2) + 2x2 * (4 + -1x2)) = 0 (32 + -8x2 + (4 * 2x2 + -1x2 * 2x2)) = 0 (32 + -8x2 + (8x2 + -2x4)) = 0 Combine like terms: -8x2 + 8x2 = 0 (32 + 0 + -2x4) = 0 (32 + -2x4) = 0 Solving 32 + -2x4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + -2x4 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -2x4 = 0 + -32 -2x4 = 0 + -32 Combine like terms: 0 + -32 = -32 -2x4 = -32 Divide each side by '-2'. 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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