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Simplifying 6n2 + 10 = -9n Reorder the terms: 10 + 6n2 = -9n Solving 10 + 6n2 = -9n Solving for variable 'n'. Reorder the terms: 10 + 9n + 6n2 = -9n + 9n Combine like terms: -9n + 9n = 0 10 + 9n + 6n2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.666666667 + 1.5n + n2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.5n + -1.666666667 + n2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.5n + n2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.5n + n2 = 0 + -1.666666667 1.5n + n2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.5n + n2 = -1.666666667 The n term is 1.5n. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5n + 0.5625 + n2 = -1.666666667 + 0.5625 Reorder the terms: 0.5625 + 1.5n + n2 = -1.666666667 + 0.5625 Combine like terms: -1.666666667 + 0.5625 = -1.104166667 0.5625 + 1.5n + n2 = -1.104166667 Factor a perfect square on the left side: (n + 0.75)(n + 0.75) = -1.104166667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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