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Simplifying (4n * 4n) + 7n + (5n * 5n) + 9n + 8 = 0 Reorder the terms for easier multiplication: (4 * 4n * n) + 7n + (5n * 5n) + 9n + 8 = 0 Multiply 4 * 4 (16n * n) + 7n + (5n * 5n) + 9n + 8 = 0 Multiply n * n (16n2) + 7n + (5n * 5n) + 9n + 8 = 0 Reorder the terms for easier multiplication: (16n2) + 7n + (5 * 5n * n) + 9n + 8 = 0 Multiply 5 * 5 (16n2) + 7n + (25n * n) + 9n + 8 = 0 Multiply n * n (16n2) + 7n + (25n2) + 9n + 8 = 0 Reorder the terms: 8 + 7n + 9n + (16n2) + (25n2) = 0 Combine like terms: 7n + 9n = 16n 8 + 16n + (16n2) + (25n2) = 0 Combine like terms: (16n2) + (25n2) = 41n2 8 + 16n + 41n2 = 0 Solving 8 + 16n + 41n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. 0.1951219512 + 0.3902439024n + n2 = 0 Move the constant term to the right: Add '-0.1951219512' to each side of the equation. 0.1951219512 + 0.3902439024n + -0.1951219512 + n2 = 0 + -0.1951219512 Reorder the terms: 0.1951219512 + -0.1951219512 + 0.3902439024n + n2 = 0 + -0.1951219512 Combine like terms: 0.1951219512 + -0.1951219512 = 0.0000000000 0.0000000000 + 0.3902439024n + n2 = 0 + -0.1951219512 0.3902439024n + n2 = 0 + -0.1951219512 Combine like terms: 0 + -0.1951219512 = -0.1951219512 0.3902439024n + n2 = -0.1951219512 The n term is 0.3902439024n. Take half its coefficient (0.1951219512). Square it (0.03807257584) and add it to both sides. Add '0.03807257584' to each side of the equation. 0.3902439024n + 0.03807257584 + n2 = -0.1951219512 + 0.03807257584 Reorder the terms: 0.03807257584 + 0.3902439024n + n2 = -0.1951219512 + 0.03807257584 Combine like terms: -0.1951219512 + 0.03807257584 = -0.15704937536 0.03807257584 + 0.3902439024n + n2 = -0.15704937536 Factor a perfect square on the left side: (n + 0.1951219512)(n + 0.1951219512) = -0.15704937536 Can't calculate square root of the right side. The solution to this equation could not be determined.
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