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Simplifying 5n2 + 19n = 3n + -92 + -3n2 Reorder the terms: 19n + 5n2 = 3n + -92 + -3n2 Reorder the terms: 19n + 5n2 = -92 + 3n + -3n2 Solving 19n + 5n2 = -92 + 3n + -3n2 Solving for variable 'n'. Reorder the terms: 92 + 19n + -3n + 5n2 + 3n2 = -92 + 3n + -3n2 + 92 + -3n + 3n2 Combine like terms: 19n + -3n = 16n 92 + 16n + 5n2 + 3n2 = -92 + 3n + -3n2 + 92 + -3n + 3n2 Combine like terms: 5n2 + 3n2 = 8n2 92 + 16n + 8n2 = -92 + 3n + -3n2 + 92 + -3n + 3n2 Reorder the terms: 92 + 16n + 8n2 = -92 + 92 + 3n + -3n + -3n2 + 3n2 Combine like terms: -92 + 92 = 0 92 + 16n + 8n2 = 0 + 3n + -3n + -3n2 + 3n2 92 + 16n + 8n2 = 3n + -3n + -3n2 + 3n2 Combine like terms: 3n + -3n = 0 92 + 16n + 8n2 = 0 + -3n2 + 3n2 92 + 16n + 8n2 = -3n2 + 3n2 Combine like terms: -3n2 + 3n2 = 0 92 + 16n + 8n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(23 + 4n + 2n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(23 + 4n + 2n2)' equal to zero and attempt to solve: Simplifying 23 + 4n + 2n2 = 0 Solving 23 + 4n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + 2n + n2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + 2n + -11.5 + n2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + 2n + n2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + 2n + n2 = 0 + -11.5 2n + n2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 2n + n2 = -11.5 The n term is 2n. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2n + 1 + n2 = -11.5 + 1 Reorder the terms: 1 + 2n + n2 = -11.5 + 1 Combine like terms: -11.5 + 1 = -10.5 1 + 2n + n2 = -10.5 Factor a perfect square on the left side: (n + 1)(n + 1) = -10.5 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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