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Simplifying n2 + 100n + -13250 = 0 Reorder the terms: -13250 + 100n + n2 = 0 Solving -13250 + 100n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '13250' to each side of the equation. -13250 + 100n + 13250 + n2 = 0 + 13250 Reorder the terms: -13250 + 13250 + 100n + n2 = 0 + 13250 Combine like terms: -13250 + 13250 = 0 0 + 100n + n2 = 0 + 13250 100n + n2 = 0 + 13250 Combine like terms: 0 + 13250 = 13250 100n + n2 = 13250 The n term is 100n. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100n + 2500 + n2 = 13250 + 2500 Reorder the terms: 2500 + 100n + n2 = 13250 + 2500 Combine like terms: 13250 + 2500 = 15750 2500 + 100n + n2 = 15750 Factor a perfect square on the left side: (n + 50)(n + 50) = 15750 Calculate the square root of the right side: 125.49900398 Break this problem into two subproblems by setting (n + 50) equal to 125.49900398 and -125.49900398.Subproblem 1
n + 50 = 125.49900398 Simplifying n + 50 = 125.49900398 Reorder the terms: 50 + n = 125.49900398 Solving 50 + n = 125.49900398 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + n = 125.49900398 + -50 Combine like terms: 50 + -50 = 0 0 + n = 125.49900398 + -50 n = 125.49900398 + -50 Combine like terms: 125.49900398 + -50 = 75.49900398 n = 75.49900398 Simplifying n = 75.49900398Subproblem 2
n + 50 = -125.49900398 Simplifying n + 50 = -125.49900398 Reorder the terms: 50 + n = -125.49900398 Solving 50 + n = -125.49900398 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + n = -125.49900398 + -50 Combine like terms: 50 + -50 = 0 0 + n = -125.49900398 + -50 n = -125.49900398 + -50 Combine like terms: -125.49900398 + -50 = -175.49900398 n = -175.49900398 Simplifying n = -175.49900398Solution
The solution to the problem is based on the solutions from the subproblems. n = {75.49900398, -175.49900398}
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