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Simplifying -8n + 4n(1 + 5n) = -6n + -14 -8n + (1 * 4n + 5n * 4n) = -6n + -14 -8n + (4n + 20n2) = -6n + -14 Combine like terms: -8n + 4n = -4n -4n + 20n2 = -6n + -14 Reorder the terms: -4n + 20n2 = -14 + -6n Solving -4n + 20n2 = -14 + -6n Solving for variable 'n'. Reorder the terms: 14 + -4n + 6n + 20n2 = -14 + -6n + 14 + 6n Combine like terms: -4n + 6n = 2n 14 + 2n + 20n2 = -14 + -6n + 14 + 6n Reorder the terms: 14 + 2n + 20n2 = -14 + 14 + -6n + 6n Combine like terms: -14 + 14 = 0 14 + 2n + 20n2 = 0 + -6n + 6n 14 + 2n + 20n2 = -6n + 6n Combine like terms: -6n + 6n = 0 14 + 2n + 20n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + n + 10n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + n + 10n2)' equal to zero and attempt to solve: Simplifying 7 + n + 10n2 = 0 Solving 7 + n + 10n2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.7 + 0.1n + n2 = 0.0 Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + 0.1n + -0.7 + n2 = 0.0 + -0.7 Reorder the terms: 0.7 + -0.7 + 0.1n + n2 = 0.0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + 0.1n + n2 = 0.0 + -0.7 0.1n + n2 = 0.0 + -0.7 Combine like terms: 0.0 + -0.7 = -0.7 0.1n + n2 = -0.7 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1n + 0.25 + n2 = -0.7 + 0.25 Reorder the terms: 0.25 + 0.1n + n2 = -0.7 + 0.25 Combine like terms: -0.7 + 0.25 = -0.45 0.25 + 0.1n + n2 = -0.45 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -0.45 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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