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Simplifying 0 = n2 + 14n + -60 Reorder the terms: 0 = -60 + 14n + n2 Solving 0 = -60 + 14n + n2 Solving for variable 'n'. Combine like terms: 0 + 60 = 60 60 + -14n + -1n2 = -60 + 14n + n2 + 60 + -14n + -1n2 Reorder the terms: 60 + -14n + -1n2 = -60 + 60 + 14n + -14n + n2 + -1n2 Combine like terms: -60 + 60 = 0 60 + -14n + -1n2 = 0 + 14n + -14n + n2 + -1n2 60 + -14n + -1n2 = 14n + -14n + n2 + -1n2 Combine like terms: 14n + -14n = 0 60 + -14n + -1n2 = 0 + n2 + -1n2 60 + -14n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 60 + -14n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + 14n + n2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 14n + 60 + n2 = 0 + 60 Reorder the terms: -60 + 60 + 14n + n2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 14n + n2 = 0 + 60 14n + n2 = 0 + 60 Combine like terms: 0 + 60 = 60 14n + n2 = 60 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 = 60 + 49 Reorder the terms: 49 + 14n + n2 = 60 + 49 Combine like terms: 60 + 49 = 109 49 + 14n + n2 = 109 Factor a perfect square on the left side: (n + 7)(n + 7) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (n + 7) equal to 10.440306509 and -10.440306509.Subproblem 1
n + 7 = 10.440306509 Simplifying n + 7 = 10.440306509 Reorder the terms: 7 + n = 10.440306509 Solving 7 + n = 10.440306509 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 = 10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + n = 10.440306509 + -7 n = 10.440306509 + -7 Combine like terms: 10.440306509 + -7 = 3.440306509 n = 3.440306509 Simplifying n = 3.440306509Subproblem 2
n + 7 = -10.440306509 Simplifying n + 7 = -10.440306509 Reorder the terms: 7 + n = -10.440306509 Solving 7 + n = -10.440306509 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 = -10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + n = -10.440306509 + -7 n = -10.440306509 + -7 Combine like terms: -10.440306509 + -7 = -17.440306509 n = -17.440306509 Simplifying n = -17.440306509Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.440306509, -17.440306509}
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