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Simplifying (15n2 + 7n + -1) + -1(4n2 + -3n + -8) = 0 Reorder the terms: (-1 + 7n + 15n2) + -1(4n2 + -3n + -8) = 0 Remove parenthesis around (-1 + 7n + 15n2) -1 + 7n + 15n2 + -1(4n2 + -3n + -8) = 0 Reorder the terms: -1 + 7n + 15n2 + -1(-8 + -3n + 4n2) = 0 -1 + 7n + 15n2 + (-8 * -1 + -3n * -1 + 4n2 * -1) = 0 -1 + 7n + 15n2 + (8 + 3n + -4n2) = 0 Reorder the terms: -1 + 8 + 7n + 3n + 15n2 + -4n2 = 0 Combine like terms: -1 + 8 = 7 7 + 7n + 3n + 15n2 + -4n2 = 0 Combine like terms: 7n + 3n = 10n 7 + 10n + 15n2 + -4n2 = 0 Combine like terms: 15n2 + -4n2 = 11n2 7 + 10n + 11n2 = 0 Solving 7 + 10n + 11n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.6363636364 + 0.9090909091n + n2 = 0 Move the constant term to the right: Add '-0.6363636364' to each side of the equation. 0.6363636364 + 0.9090909091n + -0.6363636364 + n2 = 0 + -0.6363636364 Reorder the terms: 0.6363636364 + -0.6363636364 + 0.9090909091n + n2 = 0 + -0.6363636364 Combine like terms: 0.6363636364 + -0.6363636364 = 0.0000000000 0.0000000000 + 0.9090909091n + n2 = 0 + -0.6363636364 0.9090909091n + n2 = 0 + -0.6363636364 Combine like terms: 0 + -0.6363636364 = -0.6363636364 0.9090909091n + n2 = -0.6363636364 The n term is 0.9090909091n. Take half its coefficient (0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. 0.9090909091n + 0.2066115703 + n2 = -0.6363636364 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091n + n2 = -0.6363636364 + 0.2066115703 Combine like terms: -0.6363636364 + 0.2066115703 = -0.4297520661 0.2066115703 + 0.9090909091n + n2 = -0.4297520661 Factor a perfect square on the left side: (n + 0.4545454546)(n + 0.4545454546) = -0.4297520661 Can't calculate square root of the right side. The solution to this equation could not be determined.
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