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Simplifying n2 + 12n + -49 = -10 Reorder the terms: -49 + 12n + n2 = -10 Solving -49 + 12n + n2 = -10 Solving for variable 'n'. Reorder the terms: -49 + 10 + 12n + n2 = -10 + 10 Combine like terms: -49 + 10 = -39 -39 + 12n + n2 = -10 + 10 Combine like terms: -10 + 10 = 0 -39 + 12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 12n + 39 + n2 = 0 + 39 Reorder the terms: -39 + 39 + 12n + n2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 12n + n2 = 0 + 39 12n + n2 = 0 + 39 Combine like terms: 0 + 39 = 39 12n + n2 = 39 The n term is 12n. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12n + 36 + n2 = 39 + 36 Reorder the terms: 36 + 12n + n2 = 39 + 36 Combine like terms: 39 + 36 = 75 36 + 12n + n2 = 75 Factor a perfect square on the left side: (n + 6)(n + 6) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (n + 6) equal to 8.660254038 and -8.660254038.Subproblem 1
n + 6 = 8.660254038 Simplifying n + 6 = 8.660254038 Reorder the terms: 6 + n = 8.660254038 Solving 6 + n = 8.660254038 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = 8.660254038 + -6 Combine like terms: 6 + -6 = 0 0 + n = 8.660254038 + -6 n = 8.660254038 + -6 Combine like terms: 8.660254038 + -6 = 2.660254038 n = 2.660254038 Simplifying n = 2.660254038Subproblem 2
n + 6 = -8.660254038 Simplifying n + 6 = -8.660254038 Reorder the terms: 6 + n = -8.660254038 Solving 6 + n = -8.660254038 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + n = -8.660254038 + -6 Combine like terms: 6 + -6 = 0 0 + n = -8.660254038 + -6 n = -8.660254038 + -6 Combine like terms: -8.660254038 + -6 = -14.660254038 n = -14.660254038 Simplifying n = -14.660254038Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.660254038, -14.660254038}
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