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Simplifying n2 + 14n + -56 = -10 Reorder the terms: -56 + 14n + n2 = -10 Solving -56 + 14n + n2 = -10 Solving for variable 'n'. Reorder the terms: -56 + 10 + 14n + n2 = -10 + 10 Combine like terms: -56 + 10 = -46 -46 + 14n + n2 = -10 + 10 Combine like terms: -10 + 10 = 0 -46 + 14n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 14n + 46 + n2 = 0 + 46 Reorder the terms: -46 + 46 + 14n + n2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 14n + n2 = 0 + 46 14n + n2 = 0 + 46 Combine like terms: 0 + 46 = 46 14n + n2 = 46 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 = 46 + 49 Reorder the terms: 49 + 14n + n2 = 46 + 49 Combine like terms: 46 + 49 = 95 49 + 14n + n2 = 95 Factor a perfect square on the left side: (n + 7)(n + 7) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (n + 7) equal to 9.746794345 and -9.746794345.Subproblem 1
n + 7 = 9.746794345 Simplifying n + 7 = 9.746794345 Reorder the terms: 7 + n = 9.746794345 Solving 7 + n = 9.746794345 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 = 9.746794345 + -7 Combine like terms: 7 + -7 = 0 0 + n = 9.746794345 + -7 n = 9.746794345 + -7 Combine like terms: 9.746794345 + -7 = 2.746794345 n = 2.746794345 Simplifying n = 2.746794345Subproblem 2
n + 7 = -9.746794345 Simplifying n + 7 = -9.746794345 Reorder the terms: 7 + n = -9.746794345 Solving 7 + n = -9.746794345 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 = -9.746794345 + -7 Combine like terms: 7 + -7 = 0 0 + n = -9.746794345 + -7 n = -9.746794345 + -7 Combine like terms: -9.746794345 + -7 = -16.746794345 n = -16.746794345 Simplifying n = -16.746794345Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.746794345, -16.746794345}
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