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Simplifying 5n2 + 8n = 4n + -12 Reorder the terms: 8n + 5n2 = 4n + -12 Reorder the terms: 8n + 5n2 = -12 + 4n Solving 8n + 5n2 = -12 + 4n Solving for variable 'n'. Reorder the terms: 12 + 8n + -4n + 5n2 = -12 + 4n + 12 + -4n Combine like terms: 8n + -4n = 4n 12 + 4n + 5n2 = -12 + 4n + 12 + -4n Reorder the terms: 12 + 4n + 5n2 = -12 + 12 + 4n + -4n Combine like terms: -12 + 12 = 0 12 + 4n + 5n2 = 0 + 4n + -4n 12 + 4n + 5n2 = 4n + -4n Combine like terms: 4n + -4n = 0 12 + 4n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 0.8n + n2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 0.8n + -2.4 + n2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 0.8n + n2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 0.8n + n2 = 0 + -2.4 0.8n + n2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 0.8n + n2 = -2.4 The n term is 0.8n. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8n + 0.16 + n2 = -2.4 + 0.16 Reorder the terms: 0.16 + 0.8n + n2 = -2.4 + 0.16 Combine like terms: -2.4 + 0.16 = -2.24 0.16 + 0.8n + n2 = -2.24 Factor a perfect square on the left side: (n + 0.4)(n + 0.4) = -2.24 Can't calculate square root of the right side. The solution to this equation could not be determined.
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