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Simplifying n2 + 14n + 44 = 8 Reorder the terms: 44 + 14n + n2 = 8 Solving 44 + 14n + n2 = 8 Solving for variable 'n'. Reorder the terms: 44 + -8 + 14n + n2 = 8 + -8 Combine like terms: 44 + -8 = 36 36 + 14n + n2 = 8 + -8 Combine like terms: 8 + -8 = 0 36 + 14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 14n + -36 + n2 = 0 + -36 Reorder the terms: 36 + -36 + 14n + n2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 14n + n2 = 0 + -36 14n + n2 = 0 + -36 Combine like terms: 0 + -36 = -36 14n + n2 = -36 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 = -36 + 49 Reorder the terms: 49 + 14n + n2 = -36 + 49 Combine like terms: -36 + 49 = 13 49 + 14n + n2 = 13 Factor a perfect square on the left side: (n + 7)(n + 7) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (n + 7) equal to 3.605551275 and -3.605551275.Subproblem 1
n + 7 = 3.605551275 Simplifying n + 7 = 3.605551275 Reorder the terms: 7 + n = 3.605551275 Solving 7 + n = 3.605551275 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 = 3.605551275 + -7 Combine like terms: 7 + -7 = 0 0 + n = 3.605551275 + -7 n = 3.605551275 + -7 Combine like terms: 3.605551275 + -7 = -3.394448725 n = -3.394448725 Simplifying n = -3.394448725Subproblem 2
n + 7 = -3.605551275 Simplifying n + 7 = -3.605551275 Reorder the terms: 7 + n = -3.605551275 Solving 7 + n = -3.605551275 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 = -3.605551275 + -7 Combine like terms: 7 + -7 = 0 0 + n = -3.605551275 + -7 n = -3.605551275 + -7 Combine like terms: -3.605551275 + -7 = -10.605551275 n = -10.605551275 Simplifying n = -10.605551275Solution
The solution to the problem is based on the solutions from the subproblems. n = {-3.394448725, -10.605551275}
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