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Simplifying 5n2 + 7n + 12 = -5n2 Reorder the terms: 12 + 7n + 5n2 = -5n2 Solving 12 + 7n + 5n2 = -5n2 Solving for variable 'n'. Combine like terms: 5n2 + 5n2 = 10n2 12 + 7n + 10n2 = -5n2 + 5n2 Combine like terms: -5n2 + 5n2 = 0 12 + 7n + 10n2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.2 + 0.7n + n2 = 0.0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 0.7n + -1.2 + n2 = 0.0 + -1.2 Reorder the terms: 1.2 + -1.2 + 0.7n + n2 = 0.0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 0.7n + n2 = 0.0 + -1.2 0.7n + n2 = 0.0 + -1.2 Combine like terms: 0.0 + -1.2 = -1.2 0.7n + n2 = -1.2 The n term is 0.7n. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7n + 0.1225 + n2 = -1.2 + 0.1225 Reorder the terms: 0.1225 + 0.7n + n2 = -1.2 + 0.1225 Combine like terms: -1.2 + 0.1225 = -1.0775 0.1225 + 0.7n + n2 = -1.0775 Factor a perfect square on the left side: (n + 0.35)(n + 0.35) = -1.0775 Can't calculate square root of the right side. The solution to this equation could not be determined.
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