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Simplifying (8n2 + -6n + 1) + -1(2n2 + 3n + -10) = 0 Reorder the terms: (1 + -6n + 8n2) + -1(2n2 + 3n + -10) = 0 Remove parenthesis around (1 + -6n + 8n2) 1 + -6n + 8n2 + -1(2n2 + 3n + -10) = 0 Reorder the terms: 1 + -6n + 8n2 + -1(-10 + 3n + 2n2) = 0 1 + -6n + 8n2 + (-10 * -1 + 3n * -1 + 2n2 * -1) = 0 1 + -6n + 8n2 + (10 + -3n + -2n2) = 0 Reorder the terms: 1 + 10 + -6n + -3n + 8n2 + -2n2 = 0 Combine like terms: 1 + 10 = 11 11 + -6n + -3n + 8n2 + -2n2 = 0 Combine like terms: -6n + -3n = -9n 11 + -9n + 8n2 + -2n2 = 0 Combine like terms: 8n2 + -2n2 = 6n2 11 + -9n + 6n2 = 0 Solving 11 + -9n + 6n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + -1.5n + n2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -1.5n + -1.833333333 + n2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -1.5n + n2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -1.5n + n2 = 0 + -1.833333333 -1.5n + n2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -1.5n + n2 = -1.833333333 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 = -1.833333333 + 0.5625 Reorder the terms: 0.5625 + -1.5n + n2 = -1.833333333 + 0.5625 Combine like terms: -1.833333333 + 0.5625 = -1.270833333 0.5625 + -1.5n + n2 = -1.270833333 Factor a perfect square on the left side: (n + -0.75)(n + -0.75) = -1.270833333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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