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Simplifying 3n(n) + 60n + 46 = 0 Multiply n * n 3n2 + 60n + 46 = 0 Reorder the terms: 46 + 60n + 3n2 = 0 Solving 46 + 60n + 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'. 15.33333333 + 20n + n2 = 0 Move the constant term to the right: Add '-15.33333333' to each side of the equation. 15.33333333 + 20n + -15.33333333 + n2 = 0 + -15.33333333 Reorder the terms: 15.33333333 + -15.33333333 + 20n + n2 = 0 + -15.33333333 Combine like terms: 15.33333333 + -15.33333333 = 0.00000000 0.00000000 + 20n + n2 = 0 + -15.33333333 20n + n2 = 0 + -15.33333333 Combine like terms: 0 + -15.33333333 = -15.33333333 20n + n2 = -15.33333333 The n term is 20n. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20n + 100 + n2 = -15.33333333 + 100 Reorder the terms: 100 + 20n + n2 = -15.33333333 + 100 Combine like terms: -15.33333333 + 100 = 84.66666667 100 + 20n + n2 = 84.66666667 Factor a perfect square on the left side: (n + 10)(n + 10) = 84.66666667 Calculate the square root of the right side: 9.201449161 Break this problem into two subproblems by setting (n + 10) equal to 9.201449161 and -9.201449161.Subproblem 1
n + 10 = 9.201449161 Simplifying n + 10 = 9.201449161 Reorder the terms: 10 + n = 9.201449161 Solving 10 + n = 9.201449161 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 9.201449161 + -10 Combine like terms: 10 + -10 = 0 0 + n = 9.201449161 + -10 n = 9.201449161 + -10 Combine like terms: 9.201449161 + -10 = -0.798550839 n = -0.798550839 Simplifying n = -0.798550839Subproblem 2
n + 10 = -9.201449161 Simplifying n + 10 = -9.201449161 Reorder the terms: 10 + n = -9.201449161 Solving 10 + n = -9.201449161 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = -9.201449161 + -10 Combine like terms: 10 + -10 = 0 0 + n = -9.201449161 + -10 n = -9.201449161 + -10 Combine like terms: -9.201449161 + -10 = -19.201449161 n = -19.201449161 Simplifying n = -19.201449161Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.798550839, -19.201449161}
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