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Simplifying (4x2 + -4)(4x2 + -4) = 0 Reorder the terms: (-4 + 4x2)(4x2 + -4) = 0 Reorder the terms: (-4 + 4x2)(-4 + 4x2) = 0 Multiply (-4 + 4x2) * (-4 + 4x2) (-4(-4 + 4x2) + 4x2 * (-4 + 4x2)) = 0 ((-4 * -4 + 4x2 * -4) + 4x2 * (-4 + 4x2)) = 0 ((16 + -16x2) + 4x2 * (-4 + 4x2)) = 0 (16 + -16x2 + (-4 * 4x2 + 4x2 * 4x2)) = 0 (16 + -16x2 + (-16x2 + 16x4)) = 0 Combine like terms: -16x2 + -16x2 = -32x2 (16 + -32x2 + 16x4) = 0 Solving 16 + -32x2 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(1 + -2x2 + x4) = 0 Factor a trinomial. 16((1 + -1x2)(1 + -1x2)) = 0 Factor a difference between two squares. 16(((1 + x)(1 + -1x))(1 + -1x2)) = 0 Factor a difference between two squares. 16(((1 + x)(1 + -1x))(1 + x)(1 + -1x)) = 0 Ignore the factor 16.Subproblem 1
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 2
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 = 1Subproblem 3
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 4
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, -1, 1}
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