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Simplifying 5n2 + 17n + -18 = 0 Reorder the terms: -18 + 17n + 5n2 = 0 Solving -18 + 17n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + 3.4n + n2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 3.4n + 3.6 + n2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 3.4n + n2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 3.4n + n2 = 0 + 3.6 3.4n + n2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 3.4n + n2 = 3.6 The n term is 3.4n. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4n + 2.89 + n2 = 3.6 + 2.89 Reorder the terms: 2.89 + 3.4n + n2 = 3.6 + 2.89 Combine like terms: 3.6 + 2.89 = 6.49 2.89 + 3.4n + n2 = 6.49 Factor a perfect square on the left side: (n + 1.7)(n + 1.7) = 6.49 Calculate the square root of the right side: 2.547547841 Break this problem into two subproblems by setting (n + 1.7) equal to 2.547547841 and -2.547547841.Subproblem 1
n + 1.7 = 2.547547841 Simplifying n + 1.7 = 2.547547841 Reorder the terms: 1.7 + n = 2.547547841 Solving 1.7 + n = 2.547547841 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + n = 2.547547841 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + n = 2.547547841 + -1.7 n = 2.547547841 + -1.7 Combine like terms: 2.547547841 + -1.7 = 0.847547841 n = 0.847547841 Simplifying n = 0.847547841Subproblem 2
n + 1.7 = -2.547547841 Simplifying n + 1.7 = -2.547547841 Reorder the terms: 1.7 + n = -2.547547841 Solving 1.7 + n = -2.547547841 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + n = -2.547547841 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + n = -2.547547841 + -1.7 n = -2.547547841 + -1.7 Combine like terms: -2.547547841 + -1.7 = -4.247547841 n = -4.247547841 Simplifying n = -4.247547841Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.847547841, -4.247547841}
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