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Simplifying -9 + -7n + -10n + 8n + -3n2 = 0 Combine like terms: -7n + -10n = -17n -9 + -17n + 8n + -3n2 = 0 Combine like terms: -17n + 8n = -9n -9 + -9n + -3n2 = 0 Solving -9 + -9n + -3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '-3'. -3(3 + 3n + n2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(3 + 3n + n2)' equal to zero and attempt to solve: Simplifying 3 + 3n + n2 = 0 Solving 3 + 3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + 3n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3n + n2 = 0 + -3 3n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 3n + n2 = -3 The n term is 3n. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3n + 2.25 + n2 = -3 + 2.25 Reorder the terms: 2.25 + 3n + n2 = -3 + 2.25 Combine like terms: -3 + 2.25 = -0.75 2.25 + 3n + n2 = -0.75 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = -0.75 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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