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Simplifying (n + 6)(n + 6) = 7 Reorder the terms: (6 + n)(n + 6) = 7 Reorder the terms: (6 + n)(6 + n) = 7 Multiply (6 + n) * (6 + n) (6(6 + n) + n(6 + n)) = 7 ((6 * 6 + n * 6) + n(6 + n)) = 7 ((36 + 6n) + n(6 + n)) = 7 (36 + 6n + (6 * n + n * n)) = 7 (36 + 6n + (6n + n2)) = 7 Combine like terms: 6n + 6n = 12n (36 + 12n + n2) = 7 Solving 36 + 12n + n2 = 7 Solving for variable 'n'. Reorder the terms: 36 + -7 + 12n + n2 = 7 + -7 Combine like terms: 36 + -7 = 29 29 + 12n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 29 + 12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 12n + -29 + n2 = 0 + -29 Reorder the terms: 29 + -29 + 12n + n2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 12n + n2 = 0 + -29 12n + n2 = 0 + -29 Combine like terms: 0 + -29 = -29 12n + n2 = -29 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 = -29 + 36 Reorder the terms: 36 + 12n + n2 = -29 + 36 Combine like terms: -29 + 36 = 7 36 + 12n + n2 = 7 Factor a perfect square on the left side: (n + 6)(n + 6) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (n + 6) equal to 2.645751311 and -2.645751311.Subproblem 1
n + 6 = 2.645751311 Simplifying n + 6 = 2.645751311 Reorder the terms: 6 + n = 2.645751311 Solving 6 + n = 2.645751311 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 = 2.645751311 + -6 Combine like terms: 6 + -6 = 0 0 + n = 2.645751311 + -6 n = 2.645751311 + -6 Combine like terms: 2.645751311 + -6 = -3.354248689 n = -3.354248689 Simplifying n = -3.354248689Subproblem 2
n + 6 = -2.645751311 Simplifying n + 6 = -2.645751311 Reorder the terms: 6 + n = -2.645751311 Solving 6 + n = -2.645751311 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 = -2.645751311 + -6 Combine like terms: 6 + -6 = 0 0 + n = -2.645751311 + -6 n = -2.645751311 + -6 Combine like terms: -2.645751311 + -6 = -8.645751311 n = -8.645751311 Simplifying n = -8.645751311Solution
The solution to the problem is based on the solutions from the subproblems. n = {-3.354248689, -8.645751311}
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