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Simplifying n2 + 16n + 29 = -10n Reorder the terms: 29 + 16n + n2 = -10n Solving 29 + 16n + n2 = -10n Solving for variable 'n'. Reorder the terms: 29 + 16n + 10n + n2 = -10n + 10n Combine like terms: 16n + 10n = 26n 29 + 26n + n2 = -10n + 10n Combine like terms: -10n + 10n = 0 29 + 26n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 26n + -29 + n2 = 0 + -29 Reorder the terms: 29 + -29 + 26n + n2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 26n + n2 = 0 + -29 26n + n2 = 0 + -29 Combine like terms: 0 + -29 = -29 26n + n2 = -29 The n term is 26n. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26n + 169 + n2 = -29 + 169 Reorder the terms: 169 + 26n + n2 = -29 + 169 Combine like terms: -29 + 169 = 140 169 + 26n + n2 = 140 Factor a perfect square on the left side: (n + 13)(n + 13) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (n + 13) equal to 11.832159566 and -11.832159566.Subproblem 1
n + 13 = 11.832159566 Simplifying n + 13 = 11.832159566 Reorder the terms: 13 + n = 11.832159566 Solving 13 + n = 11.832159566 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + n = 11.832159566 + -13 Combine like terms: 13 + -13 = 0 0 + n = 11.832159566 + -13 n = 11.832159566 + -13 Combine like terms: 11.832159566 + -13 = -1.167840434 n = -1.167840434 Simplifying n = -1.167840434Subproblem 2
n + 13 = -11.832159566 Simplifying n + 13 = -11.832159566 Reorder the terms: 13 + n = -11.832159566 Solving 13 + n = -11.832159566 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + n = -11.832159566 + -13 Combine like terms: 13 + -13 = 0 0 + n = -11.832159566 + -13 n = -11.832159566 + -13 Combine like terms: -11.832159566 + -13 = -24.832159566 n = -24.832159566 Simplifying n = -24.832159566Solution
The solution to the problem is based on the solutions from the subproblems. n = {-1.167840434, -24.832159566}
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