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Simplifying (n2) + -9n + -94 = -8 n2 + -9n + -94 = -8 Reorder the terms: -94 + -9n + n2 = -8 Solving -94 + -9n + n2 = -8 Solving for variable 'n'. Reorder the terms: -94 + 8 + -9n + n2 = -8 + 8 Combine like terms: -94 + 8 = -86 -86 + -9n + n2 = -8 + 8 Combine like terms: -8 + 8 = 0 -86 + -9n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + -9n + 86 + n2 = 0 + 86 Reorder the terms: -86 + 86 + -9n + n2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + -9n + n2 = 0 + 86 -9n + n2 = 0 + 86 Combine like terms: 0 + 86 = 86 -9n + n2 = 86 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 86 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 86 + 20.25 Combine like terms: 86 + 20.25 = 106.25 20.25 + -9n + n2 = 106.25 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (n + -4.5) equal to 10.307764064 and -10.307764064.Subproblem 1
n + -4.5 = 10.307764064 Simplifying n + -4.5 = 10.307764064 Reorder the terms: -4.5 + n = 10.307764064 Solving -4.5 + n = 10.307764064 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 10.307764064 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 10.307764064 + 4.5 n = 10.307764064 + 4.5 Combine like terms: 10.307764064 + 4.5 = 14.807764064 n = 14.807764064 Simplifying n = 14.807764064Subproblem 2
n + -4.5 = -10.307764064 Simplifying n + -4.5 = -10.307764064 Reorder the terms: -4.5 + n = -10.307764064 Solving -4.5 + n = -10.307764064 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -10.307764064 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -10.307764064 + 4.5 n = -10.307764064 + 4.5 Combine like terms: -10.307764064 + 4.5 = -5.807764064 n = -5.807764064 Simplifying n = -5.807764064Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.807764064, -5.807764064}
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