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Simplifying 3n2 + 11n + -600 = 0 Reorder the terms: -600 + 11n + 3n2 = 0 Solving -600 + 11n + 3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -200 + 3.666666667n + n2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 3.666666667n + 200 + n2 = 0 + 200 Reorder the terms: -200 + 200 + 3.666666667n + n2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 3.666666667n + n2 = 0 + 200 3.666666667n + n2 = 0 + 200 Combine like terms: 0 + 200 = 200 3.666666667n + n2 = 200 The n term is 3.666666667n. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667n + 3.361111114 + n2 = 200 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667n + n2 = 200 + 3.361111114 Combine like terms: 200 + 3.361111114 = 203.361111114 3.361111114 + 3.666666667n + n2 = 203.361111114 Factor a perfect square on the left side: (n + 1.833333334)(n + 1.833333334) = 203.361111114 Calculate the square root of the right side: 14.260473734 Break this problem into two subproblems by setting (n + 1.833333334) equal to 14.260473734 and -14.260473734.Subproblem 1
n + 1.833333334 = 14.260473734 Simplifying n + 1.833333334 = 14.260473734 Reorder the terms: 1.833333334 + n = 14.260473734 Solving 1.833333334 + n = 14.260473734 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + n = 14.260473734 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + n = 14.260473734 + -1.833333334 n = 14.260473734 + -1.833333334 Combine like terms: 14.260473734 + -1.833333334 = 12.4271404 n = 12.4271404 Simplifying n = 12.4271404Subproblem 2
n + 1.833333334 = -14.260473734 Simplifying n + 1.833333334 = -14.260473734 Reorder the terms: 1.833333334 + n = -14.260473734 Solving 1.833333334 + n = -14.260473734 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + n = -14.260473734 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + n = -14.260473734 + -1.833333334 n = -14.260473734 + -1.833333334 Combine like terms: -14.260473734 + -1.833333334 = -16.093807068 n = -16.093807068 Simplifying n = -16.093807068Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.4271404, -16.093807068}
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