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Simplifying n2 + 16n + -76 = 0 Reorder the terms: -76 + 16n + n2 = 0 Solving -76 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 16n + 76 + n2 = 0 + 76 Reorder the terms: -76 + 76 + 16n + n2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 16n + n2 = 0 + 76 16n + n2 = 0 + 76 Combine like terms: 0 + 76 = 76 16n + n2 = 76 The n term is 16n. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16n + 64 + n2 = 76 + 64 Reorder the terms: 64 + 16n + n2 = 76 + 64 Combine like terms: 76 + 64 = 140 64 + 16n + n2 = 140 Factor a perfect square on the left side: (n + 8)(n + 8) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (n + 8) equal to 11.832159566 and -11.832159566.Subproblem 1
n + 8 = 11.832159566 Simplifying n + 8 = 11.832159566 Reorder the terms: 8 + n = 11.832159566 Solving 8 + n = 11.832159566 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 11.832159566 + -8 Combine like terms: 8 + -8 = 0 0 + n = 11.832159566 + -8 n = 11.832159566 + -8 Combine like terms: 11.832159566 + -8 = 3.832159566 n = 3.832159566 Simplifying n = 3.832159566Subproblem 2
n + 8 = -11.832159566 Simplifying n + 8 = -11.832159566 Reorder the terms: 8 + n = -11.832159566 Solving 8 + n = -11.832159566 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = -11.832159566 + -8 Combine like terms: 8 + -8 = 0 0 + n = -11.832159566 + -8 n = -11.832159566 + -8 Combine like terms: -11.832159566 + -8 = -19.832159566 n = -19.832159566 Simplifying n = -19.832159566Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.832159566, -19.832159566}
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