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Simplifying 625 = (n + -1) * n Reorder the terms: 625 = (-1 + n) * n Reorder the terms for easier multiplication: 625 = n(-1 + n) 625 = (-1 * n + n * n) 625 = (-1n + n2) Solving 625 = -1n + n2 Solving for variable 'n'. Reorder the terms: 625 + n + -1n2 = -1n + n + n2 + -1n2 Combine like terms: -1n + n = 0 625 + n + -1n2 = 0 + n2 + -1n2 625 + n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 625 + n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -625 + -1n + n2 = 0 Move the constant term to the right: Add '625' to each side of the equation. -625 + -1n + 625 + n2 = 0 + 625 Reorder the terms: -625 + 625 + -1n + n2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + -1n + n2 = 0 + 625 -1n + n2 = 0 + 625 Combine like terms: 0 + 625 = 625 -1n + n2 = 625 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 625 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 625 + 0.25 Combine like terms: 625 + 0.25 = 625.25 0.25 + -1n + n2 = 625.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 625.25 Calculate the square root of the right side: 25.0049995 Break this problem into two subproblems by setting (n + 0.5) equal to 25.0049995 and -25.0049995.Subproblem 1
n + 0.5 = 25.0049995 Simplifying n + 0.5 = 25.0049995 Reorder the terms: 0.5 + n = 25.0049995 Solving 0.5 + n = 25.0049995 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 25.0049995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 25.0049995 + -0.5 n = 25.0049995 + -0.5 Combine like terms: 25.0049995 + -0.5 = 24.5049995 n = 24.5049995 Simplifying n = 24.5049995Subproblem 2
n + 0.5 = -25.0049995 Simplifying n + 0.5 = -25.0049995 Reorder the terms: 0.5 + n = -25.0049995 Solving 0.5 + n = -25.0049995 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -25.0049995 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -25.0049995 + -0.5 n = -25.0049995 + -0.5 Combine like terms: -25.0049995 + -0.5 = -25.5049995 n = -25.5049995 Simplifying n = -25.5049995Solution
The solution to the problem is based on the solutions from the subproblems. n = {24.5049995, -25.5049995}
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