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Simplifying n2 + 16n + 36 = 0 Reorder the terms: 36 + 16n + n2 = 0 Solving 36 + 16n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 16n + -36 + n2 = 0 + -36 Reorder the terms: 36 + -36 + 16n + n2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 16n + n2 = 0 + -36 16n + n2 = 0 + -36 Combine like terms: 0 + -36 = -36 16n + n2 = -36 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 = -36 + 64 Reorder the terms: 64 + 16n + n2 = -36 + 64 Combine like terms: -36 + 64 = 28 64 + 16n + n2 = 28 Factor a perfect square on the left side: (n + 8)(n + 8) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (n + 8) equal to 5.291502622 and -5.291502622.Subproblem 1
n + 8 = 5.291502622 Simplifying n + 8 = 5.291502622 Reorder the terms: 8 + n = 5.291502622 Solving 8 + n = 5.291502622 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 = 5.291502622 + -8 Combine like terms: 8 + -8 = 0 0 + n = 5.291502622 + -8 n = 5.291502622 + -8 Combine like terms: 5.291502622 + -8 = -2.708497378 n = -2.708497378 Simplifying n = -2.708497378Subproblem 2
n + 8 = -5.291502622 Simplifying n + 8 = -5.291502622 Reorder the terms: 8 + n = -5.291502622 Solving 8 + n = -5.291502622 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 = -5.291502622 + -8 Combine like terms: 8 + -8 = 0 0 + n = -5.291502622 + -8 n = -5.291502622 + -8 Combine like terms: -5.291502622 + -8 = -13.291502622 n = -13.291502622 Simplifying n = -13.291502622Solution
The solution to the problem is based on the solutions from the subproblems. n = {-2.708497378, -13.291502622}
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