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Simplifying n(n + 14) = -4 Reorder the terms: n(14 + n) = -4 (14 * n + n * n) = -4 (14n + n2) = -4 Solving 14n + n2 = -4 Solving for variable 'n'. Reorder the terms: 4 + 14n + n2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 14n + -4 + n2 = 0 + -4 Reorder the terms: 4 + -4 + 14n + n2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 14n + n2 = 0 + -4 14n + n2 = 0 + -4 Combine like terms: 0 + -4 = -4 14n + n2 = -4 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 = -4 + 49 Reorder the terms: 49 + 14n + n2 = -4 + 49 Combine like terms: -4 + 49 = 45 49 + 14n + n2 = 45 Factor a perfect square on the left side: (n + 7)(n + 7) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (n + 7) equal to 6.708203933 and -6.708203933.Subproblem 1
n + 7 = 6.708203933 Simplifying n + 7 = 6.708203933 Reorder the terms: 7 + n = 6.708203933 Solving 7 + n = 6.708203933 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 = 6.708203933 + -7 Combine like terms: 7 + -7 = 0 0 + n = 6.708203933 + -7 n = 6.708203933 + -7 Combine like terms: 6.708203933 + -7 = -0.291796067 n = -0.291796067 Simplifying n = -0.291796067Subproblem 2
n + 7 = -6.708203933 Simplifying n + 7 = -6.708203933 Reorder the terms: 7 + n = -6.708203933 Solving 7 + n = -6.708203933 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 = -6.708203933 + -7 Combine like terms: 7 + -7 = 0 0 + n = -6.708203933 + -7 n = -6.708203933 + -7 Combine like terms: -6.708203933 + -7 = -13.708203933 n = -13.708203933 Simplifying n = -13.708203933Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.291796067, -13.708203933}
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