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Simplifying n2 + 16n + 29 = 0 Reorder the terms: 29 + 16n + n2 = 0 Solving 29 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 16n + -29 + n2 = 0 + -29 Reorder the terms: 29 + -29 + 16n + n2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 16n + n2 = 0 + -29 16n + n2 = 0 + -29 Combine like terms: 0 + -29 = -29 16n + n2 = -29 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 = -29 + 64 Reorder the terms: 64 + 16n + n2 = -29 + 64 Combine like terms: -29 + 64 = 35 64 + 16n + n2 = 35 Factor a perfect square on the left side: (n + 8)(n + 8) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (n + 8) equal to 5.916079783 and -5.916079783.Subproblem 1
n + 8 = 5.916079783 Simplifying n + 8 = 5.916079783 Reorder the terms: 8 + n = 5.916079783 Solving 8 + n = 5.916079783 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 = 5.916079783 + -8 Combine like terms: 8 + -8 = 0 0 + n = 5.916079783 + -8 n = 5.916079783 + -8 Combine like terms: 5.916079783 + -8 = -2.083920217 n = -2.083920217 Simplifying n = -2.083920217Subproblem 2
n + 8 = -5.916079783 Simplifying n + 8 = -5.916079783 Reorder the terms: 8 + n = -5.916079783 Solving 8 + n = -5.916079783 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 = -5.916079783 + -8 Combine like terms: 8 + -8 = 0 0 + n = -5.916079783 + -8 n = -5.916079783 + -8 Combine like terms: -5.916079783 + -8 = -13.916079783 n = -13.916079783 Simplifying n = -13.916079783Solution
The solution to the problem is based on the solutions from the subproblems. n = {-2.083920217, -13.916079783}
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