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Simplifying n2 + -4n + 5 = 8 Reorder the terms: 5 + -4n + n2 = 8 Solving 5 + -4n + n2 = 8 Solving for variable 'n'. Reorder the terms: 5 + -8 + -4n + n2 = 8 + -8 Combine like terms: 5 + -8 = -3 -3 + -4n + n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -3 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -4n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + -4n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4n + n2 = 0 + 3 -4n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4n + n2 = 3 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 3 + 4 Reorder the terms: 4 + -4n + n2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4n + n2 = 7 Factor a perfect square on the left side: (n + -2)(n + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (n + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
n + -2 = 2.645751311 Simplifying n + -2 = 2.645751311 Reorder the terms: -2 + n = 2.645751311 Solving -2 + n = 2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + n = 2.645751311 + 2 n = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 n = 4.645751311 Simplifying n = 4.645751311Subproblem 2
n + -2 = -2.645751311 Simplifying n + -2 = -2.645751311 Reorder the terms: -2 + n = -2.645751311 Solving -2 + n = -2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + n = -2.645751311 + 2 n = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 n = -0.645751311 Simplifying n = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.645751311, -0.645751311}
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