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Simplifying 0 = x4 + 32x2 + 256 Reorder the terms: 0 = 256 + 32x2 + x4 Solving 0 = 256 + 32x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -256 = -256 -256 + -32x2 + -1x4 = 256 + 32x2 + x4 + -256 + -32x2 + -1x4 Reorder the terms: -256 + -32x2 + -1x4 = 256 + -256 + 32x2 + -32x2 + x4 + -1x4 Combine like terms: 256 + -256 = 0 -256 + -32x2 + -1x4 = 0 + 32x2 + -32x2 + x4 + -1x4 -256 + -32x2 + -1x4 = 32x2 + -32x2 + x4 + -1x4 Combine like terms: 32x2 + -32x2 = 0 -256 + -32x2 + -1x4 = 0 + x4 + -1x4 -256 + -32x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -256 + -32x2 + -1x4 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(256 + 32x2 + x4) = 0 Factor a trinomial. -1((16 + x2)(16 + x2)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + x2)' equal to zero and attempt to solve: Simplifying 16 + x2 = 0 Solving 16 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x2 = 0 + -16 x2 = 0 + -16 Combine like terms: 0 + -16 = -16 x2 = -16 Simplifying x2 = -16 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 '(16 + x2)' equal to zero and attempt to solve: Simplifying 16 + x2 = 0 Solving 16 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x2 = 0 + -16 x2 = 0 + -16 Combine like terms: 0 + -16 = -16 x2 = -16 Simplifying x2 = -16 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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