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Simplifying n2 + 16n + -87 = 7 Reorder the terms: -87 + 16n + n2 = 7 Solving -87 + 16n + n2 = 7 Solving for variable 'n'. Reorder the terms: -87 + -7 + 16n + n2 = 7 + -7 Combine like terms: -87 + -7 = -94 -94 + 16n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -94 + 16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + 16n + 94 + n2 = 0 + 94 Reorder the terms: -94 + 94 + 16n + n2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 16n + n2 = 0 + 94 16n + n2 = 0 + 94 Combine like terms: 0 + 94 = 94 16n + n2 = 94 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 = 94 + 64 Reorder the terms: 64 + 16n + n2 = 94 + 64 Combine like terms: 94 + 64 = 158 64 + 16n + n2 = 158 Factor a perfect square on the left side: (n + 8)(n + 8) = 158 Calculate the square root of the right side: 12.56980509 Break this problem into two subproblems by setting (n + 8) equal to 12.56980509 and -12.56980509.Subproblem 1
n + 8 = 12.56980509 Simplifying n + 8 = 12.56980509 Reorder the terms: 8 + n = 12.56980509 Solving 8 + n = 12.56980509 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 = 12.56980509 + -8 Combine like terms: 8 + -8 = 0 0 + n = 12.56980509 + -8 n = 12.56980509 + -8 Combine like terms: 12.56980509 + -8 = 4.56980509 n = 4.56980509 Simplifying n = 4.56980509Subproblem 2
n + 8 = -12.56980509 Simplifying n + 8 = -12.56980509 Reorder the terms: 8 + n = -12.56980509 Solving 8 + n = -12.56980509 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 = -12.56980509 + -8 Combine like terms: 8 + -8 = 0 0 + n = -12.56980509 + -8 n = -12.56980509 + -8 Combine like terms: -12.56980509 + -8 = -20.56980509 n = -20.56980509 Simplifying n = -20.56980509Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.56980509, -20.56980509}
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