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Simplifying n(17 + 5n) = 900 (17 * n + 5n * n) = 900 (17n + 5n2) = 900 Solving 17n + 5n2 = 900 Solving for variable 'n'. Reorder the terms: -900 + 17n + 5n2 = 900 + -900 Combine like terms: 900 + -900 = 0 -900 + 17n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -180 + 3.4n + n2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 3.4n + 180 + n2 = 0 + 180 Reorder the terms: -180 + 180 + 3.4n + n2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 3.4n + n2 = 0 + 180 3.4n + n2 = 0 + 180 Combine like terms: 0 + 180 = 180 3.4n + n2 = 180 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 = 180 + 2.89 Reorder the terms: 2.89 + 3.4n + n2 = 180 + 2.89 Combine like terms: 180 + 2.89 = 182.89 2.89 + 3.4n + n2 = 182.89 Factor a perfect square on the left side: (n + 1.7)(n + 1.7) = 182.89 Calculate the square root of the right side: 13.52368293 Break this problem into two subproblems by setting (n + 1.7) equal to 13.52368293 and -13.52368293.Subproblem 1
n + 1.7 = 13.52368293 Simplifying n + 1.7 = 13.52368293 Reorder the terms: 1.7 + n = 13.52368293 Solving 1.7 + n = 13.52368293 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 = 13.52368293 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + n = 13.52368293 + -1.7 n = 13.52368293 + -1.7 Combine like terms: 13.52368293 + -1.7 = 11.82368293 n = 11.82368293 Simplifying n = 11.82368293Subproblem 2
n + 1.7 = -13.52368293 Simplifying n + 1.7 = -13.52368293 Reorder the terms: 1.7 + n = -13.52368293 Solving 1.7 + n = -13.52368293 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 = -13.52368293 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + n = -13.52368293 + -1.7 n = -13.52368293 + -1.7 Combine like terms: -13.52368293 + -1.7 = -15.22368293 n = -15.22368293 Simplifying n = -15.22368293Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.82368293, -15.22368293}
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