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Simplifying 5n2 + 8n + 42 = 0 Reorder the terms: 42 + 8n + 5n2 = 0 Solving 42 + 8n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.4 + 1.6n + n2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + 1.6n + -8.4 + n2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + 1.6n + n2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + 1.6n + n2 = 0 + -8.4 1.6n + n2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 1.6n + n2 = -8.4 The n term is 1.6n. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6n + 0.64 + n2 = -8.4 + 0.64 Reorder the terms: 0.64 + 1.6n + n2 = -8.4 + 0.64 Combine like terms: -8.4 + 0.64 = -7.76 0.64 + 1.6n + n2 = -7.76 Factor a perfect square on the left side: (n + 0.8)(n + 0.8) = -7.76 Can't calculate square root of the right side. The solution to this equation could not be determined.
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