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Simplifying n2 + -23n + 2 = 0 Reorder the terms: 2 + -23n + n2 = 0 Solving 2 + -23n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -23n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + -23n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -23n + n2 = 0 + -2 -23n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -23n + n2 = -2 The n term is -23n. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23n + 132.25 + n2 = -2 + 132.25 Reorder the terms: 132.25 + -23n + n2 = -2 + 132.25 Combine like terms: -2 + 132.25 = 130.25 132.25 + -23n + n2 = 130.25 Factor a perfect square on the left side: (n + -11.5)(n + -11.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (n + -11.5) equal to 11.412712211 and -11.412712211.Subproblem 1
n + -11.5 = 11.412712211 Simplifying n + -11.5 = 11.412712211 Reorder the terms: -11.5 + n = 11.412712211 Solving -11.5 + n = 11.412712211 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + n = 11.412712211 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + n = 11.412712211 + 11.5 n = 11.412712211 + 11.5 Combine like terms: 11.412712211 + 11.5 = 22.912712211 n = 22.912712211 Simplifying n = 22.912712211Subproblem 2
n + -11.5 = -11.412712211 Simplifying n + -11.5 = -11.412712211 Reorder the terms: -11.5 + n = -11.412712211 Solving -11.5 + n = -11.412712211 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + n = -11.412712211 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + n = -11.412712211 + 11.5 n = -11.412712211 + 11.5 Combine like terms: -11.412712211 + 11.5 = 0.087287789 n = 0.087287789 Simplifying n = 0.087287789Solution
The solution to the problem is based on the solutions from the subproblems. n = {22.912712211, 0.087287789}
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