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Simplifying 2n2 = -16 + -8n Solving 2n2 = -16 + -8n Solving for variable 'n'. Reorder the terms: 16 + 8n + 2n2 = -16 + -8n + 16 + 8n Reorder the terms: 16 + 8n + 2n2 = -16 + 16 + -8n + 8n Combine like terms: -16 + 16 = 0 16 + 8n + 2n2 = 0 + -8n + 8n 16 + 8n + 2n2 = -8n + 8n Combine like terms: -8n + 8n = 0 16 + 8n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 4n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 4n + n2)' equal to zero and attempt to solve: Simplifying 8 + 4n + n2 = 0 Solving 8 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 4n + -8 + n2 = 0 + -8 Reorder the terms: 8 + -8 + 4n + n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 4n + n2 = 0 + -8 4n + n2 = 0 + -8 Combine like terms: 0 + -8 = -8 4n + n2 = -8 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = -8 + 4 Reorder the terms: 4 + 4n + n2 = -8 + 4 Combine like terms: -8 + 4 = -4 4 + 4n + n2 = -4 Factor a perfect square on the left side: (n + 2)(n + 2) = -4 Can't calculate square root of the right side. 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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