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Simplifying -1n2 + -8n + -31 = 0 Reorder the terms: -31 + -8n + -1n2 = 0 Solving -31 + -8n + -1n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-1'. -1(31 + 8n + n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(31 + 8n + n2)' equal to zero and attempt to solve: Simplifying 31 + 8n + n2 = 0 Solving 31 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 8n + -31 + n2 = 0 + -31 Reorder the terms: 31 + -31 + 8n + n2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 8n + n2 = 0 + -31 8n + n2 = 0 + -31 Combine like terms: 0 + -31 = -31 8n + n2 = -31 The n term is 8n. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8n + 16 + n2 = -31 + 16 Reorder the terms: 16 + 8n + n2 = -31 + 16 Combine like terms: -31 + 16 = -15 16 + 8n + n2 = -15 Factor a perfect square on the left side: (n + 4)(n + 4) = -15 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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