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Simplifying 2n2 + 6n + 2 = -8 Reorder the terms: 2 + 6n + 2n2 = -8 Solving 2 + 6n + 2n2 = -8 Solving for variable 'n'. Reorder the terms: 2 + 8 + 6n + 2n2 = -8 + 8 Combine like terms: 2 + 8 = 10 10 + 6n + 2n2 = -8 + 8 Combine like terms: -8 + 8 = 0 10 + 6n + 2n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 3n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 3n + n2)' equal to zero and attempt to solve: Simplifying 5 + 3n + n2 = 0 Solving 5 + 3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 3n + -5 + n2 = 0 + -5 Reorder the terms: 5 + -5 + 3n + n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3n + n2 = 0 + -5 3n + n2 = 0 + -5 Combine like terms: 0 + -5 = -5 3n + n2 = -5 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 = -5 + 2.25 Reorder the terms: 2.25 + 3n + n2 = -5 + 2.25 Combine like terms: -5 + 2.25 = -2.75 2.25 + 3n + n2 = -2.75 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = -2.75 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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