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Simplifying n2 + -11n + 10 = 1 Reorder the terms: 10 + -11n + n2 = 1 Solving 10 + -11n + n2 = 1 Solving for variable 'n'. Reorder the terms: 10 + -1 + -11n + n2 = 1 + -1 Combine like terms: 10 + -1 = 9 9 + -11n + n2 = 1 + -1 Combine like terms: 1 + -1 = 0 9 + -11n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -11n + -9 + n2 = 0 + -9 Reorder the terms: 9 + -9 + -11n + n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -11n + n2 = 0 + -9 -11n + n2 = 0 + -9 Combine like terms: 0 + -9 = -9 -11n + n2 = -9 The n term is -11n. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11n + 30.25 + n2 = -9 + 30.25 Reorder the terms: 30.25 + -11n + n2 = -9 + 30.25 Combine like terms: -9 + 30.25 = 21.25 30.25 + -11n + n2 = 21.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (n + -5.5) equal to 4.609772229 and -4.609772229.Subproblem 1
n + -5.5 = 4.609772229 Simplifying n + -5.5 = 4.609772229 Reorder the terms: -5.5 + n = 4.609772229 Solving -5.5 + n = 4.609772229 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 4.609772229 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 4.609772229 + 5.5 n = 4.609772229 + 5.5 Combine like terms: 4.609772229 + 5.5 = 10.109772229 n = 10.109772229 Simplifying n = 10.109772229Subproblem 2
n + -5.5 = -4.609772229 Simplifying n + -5.5 = -4.609772229 Reorder the terms: -5.5 + n = -4.609772229 Solving -5.5 + n = -4.609772229 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -4.609772229 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -4.609772229 + 5.5 n = -4.609772229 + 5.5 Combine like terms: -4.609772229 + 5.5 = 0.890227771 n = 0.890227771 Simplifying n = 0.890227771Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.109772229, 0.890227771}
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