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Simplifying n2 + 14n = -22 Reorder the terms: 14n + n2 = -22 Solving 14n + n2 = -22 Solving for variable 'n'. Reorder the terms: 22 + 14n + n2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + 14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 14n + -22 + n2 = 0 + -22 Reorder the terms: 22 + -22 + 14n + n2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 14n + n2 = 0 + -22 14n + n2 = 0 + -22 Combine like terms: 0 + -22 = -22 14n + n2 = -22 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 = -22 + 49 Reorder the terms: 49 + 14n + n2 = -22 + 49 Combine like terms: -22 + 49 = 27 49 + 14n + n2 = 27 Factor a perfect square on the left side: (n + 7)(n + 7) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (n + 7) equal to 5.196152423 and -5.196152423.Subproblem 1
n + 7 = 5.196152423 Simplifying n + 7 = 5.196152423 Reorder the terms: 7 + n = 5.196152423 Solving 7 + n = 5.196152423 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 = 5.196152423 + -7 Combine like terms: 7 + -7 = 0 0 + n = 5.196152423 + -7 n = 5.196152423 + -7 Combine like terms: 5.196152423 + -7 = -1.803847577 n = -1.803847577 Simplifying n = -1.803847577Subproblem 2
n + 7 = -5.196152423 Simplifying n + 7 = -5.196152423 Reorder the terms: 7 + n = -5.196152423 Solving 7 + n = -5.196152423 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 = -5.196152423 + -7 Combine like terms: 7 + -7 = 0 0 + n = -5.196152423 + -7 n = -5.196152423 + -7 Combine like terms: -5.196152423 + -7 = -12.196152423 n = -12.196152423 Simplifying n = -12.196152423Solution
The solution to the problem is based on the solutions from the subproblems. n = {-1.803847577, -12.196152423}
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