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Simplifying n2 + 16n + -7 = 2 Reorder the terms: -7 + 16n + n2 = 2 Solving -7 + 16n + n2 = 2 Solving for variable 'n'. Reorder the terms: -7 + -2 + 16n + n2 = 2 + -2 Combine like terms: -7 + -2 = -9 -9 + 16n + n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -9 + 16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 16n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + 16n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 16n + n2 = 0 + 9 16n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 16n + n2 = 9 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 = 9 + 64 Reorder the terms: 64 + 16n + n2 = 9 + 64 Combine like terms: 9 + 64 = 73 64 + 16n + n2 = 73 Factor a perfect square on the left side: (n + 8)(n + 8) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (n + 8) equal to 8.544003745 and -8.544003745.Subproblem 1
n + 8 = 8.544003745 Simplifying n + 8 = 8.544003745 Reorder the terms: 8 + n = 8.544003745 Solving 8 + n = 8.544003745 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 = 8.544003745 + -8 Combine like terms: 8 + -8 = 0 0 + n = 8.544003745 + -8 n = 8.544003745 + -8 Combine like terms: 8.544003745 + -8 = 0.544003745 n = 0.544003745 Simplifying n = 0.544003745Subproblem 2
n + 8 = -8.544003745 Simplifying n + 8 = -8.544003745 Reorder the terms: 8 + n = -8.544003745 Solving 8 + n = -8.544003745 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 = -8.544003745 + -8 Combine like terms: 8 + -8 = 0 0 + n = -8.544003745 + -8 n = -8.544003745 + -8 Combine like terms: -8.544003745 + -8 = -16.544003745 n = -16.544003745 Simplifying n = -16.544003745Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.544003745, -16.544003745}
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