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Simplifying n2 + 23n + -100 = 0 Reorder the terms: -100 + 23n + n2 = 0 Solving -100 + 23n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 23n + 100 + n2 = 0 + 100 Reorder the terms: -100 + 100 + 23n + n2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 23n + n2 = 0 + 100 23n + n2 = 0 + 100 Combine like terms: 0 + 100 = 100 23n + n2 = 100 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 = 100 + 132.25 Reorder the terms: 132.25 + 23n + n2 = 100 + 132.25 Combine like terms: 100 + 132.25 = 232.25 132.25 + 23n + n2 = 232.25 Factor a perfect square on the left side: (n + 11.5)(n + 11.5) = 232.25 Calculate the square root of the right side: 15.239750654 Break this problem into two subproblems by setting (n + 11.5) equal to 15.239750654 and -15.239750654.Subproblem 1
n + 11.5 = 15.239750654 Simplifying n + 11.5 = 15.239750654 Reorder the terms: 11.5 + n = 15.239750654 Solving 11.5 + n = 15.239750654 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 = 15.239750654 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + n = 15.239750654 + -11.5 n = 15.239750654 + -11.5 Combine like terms: 15.239750654 + -11.5 = 3.739750654 n = 3.739750654 Simplifying n = 3.739750654Subproblem 2
n + 11.5 = -15.239750654 Simplifying n + 11.5 = -15.239750654 Reorder the terms: 11.5 + n = -15.239750654 Solving 11.5 + n = -15.239750654 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 = -15.239750654 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + n = -15.239750654 + -11.5 n = -15.239750654 + -11.5 Combine like terms: -15.239750654 + -11.5 = -26.739750654 n = -26.739750654 Simplifying n = -26.739750654Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.739750654, -26.739750654}
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