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Simplifying n2 + -14n + 49 = 6 Reorder the terms: 49 + -14n + n2 = 6 Solving 49 + -14n + n2 = 6 Solving for variable 'n'. Reorder the terms: 49 + -6 + -14n + n2 = 6 + -6 Combine like terms: 49 + -6 = 43 43 + -14n + n2 = 6 + -6 Combine like terms: 6 + -6 = 0 43 + -14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -14n + -43 + n2 = 0 + -43 Reorder the terms: 43 + -43 + -14n + n2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -14n + n2 = 0 + -43 -14n + n2 = 0 + -43 Combine like terms: 0 + -43 = -43 -14n + n2 = -43 The n term is -14n. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14n + 49 + n2 = -43 + 49 Reorder the terms: 49 + -14n + n2 = -43 + 49 Combine like terms: -43 + 49 = 6 49 + -14n + n2 = 6 Factor a perfect square on the left side: (n + -7)(n + -7) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (n + -7) equal to 2.449489743 and -2.449489743.Subproblem 1
n + -7 = 2.449489743 Simplifying n + -7 = 2.449489743 Reorder the terms: -7 + n = 2.449489743 Solving -7 + n = 2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = 2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + n = 2.449489743 + 7 n = 2.449489743 + 7 Combine like terms: 2.449489743 + 7 = 9.449489743 n = 9.449489743 Simplifying n = 9.449489743Subproblem 2
n + -7 = -2.449489743 Simplifying n + -7 = -2.449489743 Reorder the terms: -7 + n = -2.449489743 Solving -7 + n = -2.449489743 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = -2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + n = -2.449489743 + 7 n = -2.449489743 + 7 Combine like terms: -2.449489743 + 7 = 4.550510257 n = 4.550510257 Simplifying n = 4.550510257Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.449489743, 4.550510257}
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