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Simplifying n(n + 14) = -5 Reorder the terms: n(14 + n) = -5 (14 * n + n * n) = -5 (14n + n2) = -5 Solving 14n + n2 = -5 Solving for variable 'n'. Reorder the terms: 5 + 14n + n2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 14n + -5 + n2 = 0 + -5 Reorder the terms: 5 + -5 + 14n + n2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 14n + n2 = 0 + -5 14n + n2 = 0 + -5 Combine like terms: 0 + -5 = -5 14n + n2 = -5 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 = -5 + 49 Reorder the terms: 49 + 14n + n2 = -5 + 49 Combine like terms: -5 + 49 = 44 49 + 14n + n2 = 44 Factor a perfect square on the left side: (n + 7)(n + 7) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (n + 7) equal to 6.633249581 and -6.633249581.Subproblem 1
n + 7 = 6.633249581 Simplifying n + 7 = 6.633249581 Reorder the terms: 7 + n = 6.633249581 Solving 7 + n = 6.633249581 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 = 6.633249581 + -7 Combine like terms: 7 + -7 = 0 0 + n = 6.633249581 + -7 n = 6.633249581 + -7 Combine like terms: 6.633249581 + -7 = -0.366750419 n = -0.366750419 Simplifying n = -0.366750419Subproblem 2
n + 7 = -6.633249581 Simplifying n + 7 = -6.633249581 Reorder the terms: 7 + n = -6.633249581 Solving 7 + n = -6.633249581 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 = -6.633249581 + -7 Combine like terms: 7 + -7 = 0 0 + n = -6.633249581 + -7 n = -6.633249581 + -7 Combine like terms: -6.633249581 + -7 = -13.633249581 n = -13.633249581 Simplifying n = -13.633249581Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.366750419, -13.633249581}
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