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Simplifying 5n2 + 17n + -52 = 0 Reorder the terms: -52 + 17n + 5n2 = 0 Solving -52 + 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'. -10.4 + 3.4n + n2 = 0 Move the constant term to the right: Add '10.4' to each side of the equation. -10.4 + 3.4n + 10.4 + n2 = 0 + 10.4 Reorder the terms: -10.4 + 10.4 + 3.4n + n2 = 0 + 10.4 Combine like terms: -10.4 + 10.4 = 0.0 0.0 + 3.4n + n2 = 0 + 10.4 3.4n + n2 = 0 + 10.4 Combine like terms: 0 + 10.4 = 10.4 3.4n + n2 = 10.4 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 = 10.4 + 2.89 Reorder the terms: 2.89 + 3.4n + n2 = 10.4 + 2.89 Combine like terms: 10.4 + 2.89 = 13.29 2.89 + 3.4n + n2 = 13.29 Factor a perfect square on the left side: (n + 1.7)(n + 1.7) = 13.29 Calculate the square root of the right side: 3.645545227 Break this problem into two subproblems by setting (n + 1.7) equal to 3.645545227 and -3.645545227.Subproblem 1
n + 1.7 = 3.645545227 Simplifying n + 1.7 = 3.645545227 Reorder the terms: 1.7 + n = 3.645545227 Solving 1.7 + n = 3.645545227 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 = 3.645545227 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + n = 3.645545227 + -1.7 n = 3.645545227 + -1.7 Combine like terms: 3.645545227 + -1.7 = 1.945545227 n = 1.945545227 Simplifying n = 1.945545227Subproblem 2
n + 1.7 = -3.645545227 Simplifying n + 1.7 = -3.645545227 Reorder the terms: 1.7 + n = -3.645545227 Solving 1.7 + n = -3.645545227 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 = -3.645545227 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + n = -3.645545227 + -1.7 n = -3.645545227 + -1.7 Combine like terms: -3.645545227 + -1.7 = -5.345545227 n = -5.345545227 Simplifying n = -5.345545227Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.945545227, -5.345545227}
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