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Simplifying 0 = n2 + 7n + 60 Reorder the terms: 0 = 60 + 7n + n2 Solving 0 = 60 + 7n + n2 Solving for variable 'n'. Combine like terms: 0 + -60 = -60 -60 + -7n + -1n2 = 60 + 7n + n2 + -60 + -7n + -1n2 Reorder the terms: -60 + -7n + -1n2 = 60 + -60 + 7n + -7n + n2 + -1n2 Combine like terms: 60 + -60 = 0 -60 + -7n + -1n2 = 0 + 7n + -7n + n2 + -1n2 -60 + -7n + -1n2 = 7n + -7n + n2 + -1n2 Combine like terms: 7n + -7n = 0 -60 + -7n + -1n2 = 0 + n2 + -1n2 -60 + -7n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -60 + -7n + -1n2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 7n + n2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(60 + 7n + n2)' equal to zero and attempt to solve: Simplifying 60 + 7n + n2 = 0 Solving 60 + 7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 7n + -60 + n2 = 0 + -60 Reorder the terms: 60 + -60 + 7n + n2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 7n + n2 = 0 + -60 7n + n2 = 0 + -60 Combine like terms: 0 + -60 = -60 7n + n2 = -60 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = -60 + 12.25 Reorder the terms: 12.25 + 7n + n2 = -60 + 12.25 Combine like terms: -60 + 12.25 = -47.75 12.25 + 7n + n2 = -47.75 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = -47.75 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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