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Simplifying n2 + 16n + 64 = 30 Reorder the terms: 64 + 16n + n2 = 30 Solving 64 + 16n + n2 = 30 Solving for variable 'n'. Reorder the terms: 64 + -30 + 16n + n2 = 30 + -30 Combine like terms: 64 + -30 = 34 34 + 16n + n2 = 30 + -30 Combine like terms: 30 + -30 = 0 34 + 16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + 16n + -34 + n2 = 0 + -34 Reorder the terms: 34 + -34 + 16n + n2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 16n + n2 = 0 + -34 16n + n2 = 0 + -34 Combine like terms: 0 + -34 = -34 16n + n2 = -34 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 = -34 + 64 Reorder the terms: 64 + 16n + n2 = -34 + 64 Combine like terms: -34 + 64 = 30 64 + 16n + n2 = 30 Factor a perfect square on the left side: (n + 8)(n + 8) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (n + 8) equal to 5.477225575 and -5.477225575.Subproblem 1
n + 8 = 5.477225575 Simplifying n + 8 = 5.477225575 Reorder the terms: 8 + n = 5.477225575 Solving 8 + n = 5.477225575 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 = 5.477225575 + -8 Combine like terms: 8 + -8 = 0 0 + n = 5.477225575 + -8 n = 5.477225575 + -8 Combine like terms: 5.477225575 + -8 = -2.522774425 n = -2.522774425 Simplifying n = -2.522774425Subproblem 2
n + 8 = -5.477225575 Simplifying n + 8 = -5.477225575 Reorder the terms: 8 + n = -5.477225575 Solving 8 + n = -5.477225575 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 = -5.477225575 + -8 Combine like terms: 8 + -8 = 0 0 + n = -5.477225575 + -8 n = -5.477225575 + -8 Combine like terms: -5.477225575 + -8 = -13.477225575 n = -13.477225575 Simplifying n = -13.477225575Solution
The solution to the problem is based on the solutions from the subproblems. n = {-2.522774425, -13.477225575}
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