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Simplifying n2 + 16n + -49 = 0 Reorder the terms: -49 + 16n + n2 = 0 Solving -49 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 16n + 49 + n2 = 0 + 49 Reorder the terms: -49 + 49 + 16n + n2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 16n + n2 = 0 + 49 16n + n2 = 0 + 49 Combine like terms: 0 + 49 = 49 16n + n2 = 49 The n term is 16n. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16n + 64 + n2 = 49 + 64 Reorder the terms: 64 + 16n + n2 = 49 + 64 Combine like terms: 49 + 64 = 113 64 + 16n + n2 = 113 Factor a perfect square on the left side: (n + 8)(n + 8) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (n + 8) equal to 10.630145813 and -10.630145813.Subproblem 1
n + 8 = 10.630145813 Simplifying n + 8 = 10.630145813 Reorder the terms: 8 + n = 10.630145813 Solving 8 + n = 10.630145813 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 10.630145813 + -8 Combine like terms: 8 + -8 = 0 0 + n = 10.630145813 + -8 n = 10.630145813 + -8 Combine like terms: 10.630145813 + -8 = 2.630145813 n = 2.630145813 Simplifying n = 2.630145813Subproblem 2
n + 8 = -10.630145813 Simplifying n + 8 = -10.630145813 Reorder the terms: 8 + n = -10.630145813 Solving 8 + n = -10.630145813 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = -10.630145813 + -8 Combine like terms: 8 + -8 = 0 0 + n = -10.630145813 + -8 n = -10.630145813 + -8 Combine like terms: -10.630145813 + -8 = -18.630145813 n = -18.630145813 Simplifying n = -18.630145813Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.630145813, -18.630145813}
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