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Simplifying n2 + 16n = 7 Reorder the terms: 16n + n2 = 7 Solving 16n + n2 = 7 Solving for variable 'n'. Reorder the terms: -7 + 16n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 16n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + 16n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 16n + n2 = 0 + 7 16n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 16n + n2 = 7 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 = 7 + 64 Reorder the terms: 64 + 16n + n2 = 7 + 64 Combine like terms: 7 + 64 = 71 64 + 16n + n2 = 71 Factor a perfect square on the left side: (n + 8)(n + 8) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (n + 8) equal to 8.426149773 and -8.426149773.Subproblem 1
n + 8 = 8.426149773 Simplifying n + 8 = 8.426149773 Reorder the terms: 8 + n = 8.426149773 Solving 8 + n = 8.426149773 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 = 8.426149773 + -8 Combine like terms: 8 + -8 = 0 0 + n = 8.426149773 + -8 n = 8.426149773 + -8 Combine like terms: 8.426149773 + -8 = 0.426149773 n = 0.426149773 Simplifying n = 0.426149773Subproblem 2
n + 8 = -8.426149773 Simplifying n + 8 = -8.426149773 Reorder the terms: 8 + n = -8.426149773 Solving 8 + n = -8.426149773 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 = -8.426149773 + -8 Combine like terms: 8 + -8 = 0 0 + n = -8.426149773 + -8 n = -8.426149773 + -8 Combine like terms: -8.426149773 + -8 = -16.426149773 n = -16.426149773 Simplifying n = -16.426149773Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.426149773, -16.426149773}
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