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Simplifying x2(x2 + -16) + -1(x2 + -16) = 0 Reorder the terms: x2(-16 + x2) + -1(x2 + -16) = 0 (-16 * x2 + x2 * x2) + -1(x2 + -16) = 0 (-16x2 + x4) + -1(x2 + -16) = 0 Reorder the terms: -16x2 + x4 + -1(-16 + x2) = 0 -16x2 + x4 + (-16 * -1 + x2 * -1) = 0 -16x2 + x4 + (16 + -1x2) = 0 Reorder the terms: 16 + -16x2 + -1x2 + x4 = 0 Combine like terms: -16x2 + -1x2 = -17x2 16 + -17x2 + x4 = 0 Solving 16 + -17x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x2)(16 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(16 + -1x2) = 0 Factor a difference between two squares. ((4 + x)(4 + -1x))(1 + x)(1 + -1x) = 0Subproblem 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 4
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-1, 1, -4, 4}
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