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Simplifying (2n2 + -4n + 9) + -1(-6n2 + -7n + 5) = 0 Reorder the terms: (9 + -4n + 2n2) + -1(-6n2 + -7n + 5) = 0 Remove parenthesis around (9 + -4n + 2n2) 9 + -4n + 2n2 + -1(-6n2 + -7n + 5) = 0 Reorder the terms: 9 + -4n + 2n2 + -1(5 + -7n + -6n2) = 0 9 + -4n + 2n2 + (5 * -1 + -7n * -1 + -6n2 * -1) = 0 9 + -4n + 2n2 + (-5 + 7n + 6n2) = 0 Reorder the terms: 9 + -5 + -4n + 7n + 2n2 + 6n2 = 0 Combine like terms: 9 + -5 = 4 4 + -4n + 7n + 2n2 + 6n2 = 0 Combine like terms: -4n + 7n = 3n 4 + 3n + 2n2 + 6n2 = 0 Combine like terms: 2n2 + 6n2 = 8n2 4 + 3n + 8n2 = 0 Solving 4 + 3n + 8n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.5 + 0.375n + n2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.375n + -0.5 + n2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.375n + n2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.375n + n2 = 0 + -0.5 0.375n + n2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.375n + n2 = -0.5 The n term is 0.375n. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375n + 0.03515625 + n2 = -0.5 + 0.03515625 Reorder the terms: 0.03515625 + 0.375n + n2 = -0.5 + 0.03515625 Combine like terms: -0.5 + 0.03515625 = -0.46484375 0.03515625 + 0.375n + n2 = -0.46484375 Factor a perfect square on the left side: (n + 0.1875)(n + 0.1875) = -0.46484375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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