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Simplifying (25n2) + 10n + -1 = 0 Reorder the terms: -1 + 10n + (25n2) = 0 Solving -1 + 10n + (25n2) = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + 0.4n + n2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + 0.4n + 0.04 + n2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + 0.4n + n2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + 0.4n + n2 = 0 + 0.04 0.4n + n2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 0.4n + n2 = 0.04 The n term is 0.4n. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4n + 0.04 + n2 = 0.04 + 0.04 Reorder the terms: 0.04 + 0.4n + n2 = 0.04 + 0.04 Combine like terms: 0.04 + 0.04 = 0.08 0.04 + 0.4n + n2 = 0.08 Factor a perfect square on the left side: ((n) + 0.2)((n) + 0.2) = 0.08 Calculate the square root of the right side: 0.282842712 Break this problem into two subproblems by setting ((n) + 0.2) equal to 0.282842712 and -0.282842712.Subproblem 1
(n) + 0.2 = 0.282842712 Simplifying (n) + 0.2 = 0.282842712 n + 0.2 = 0.282842712 Reorder the terms: 0.2 + n = 0.282842712 Solving 0.2 + n = 0.282842712 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + n = 0.282842712 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + n = 0.282842712 + -0.2 n = 0.282842712 + -0.2 Combine like terms: 0.282842712 + -0.2 = 0.082842712 n = 0.082842712 Simplifying n = 0.082842712Subproblem 2
(n) + 0.2 = -0.282842712 Simplifying (n) + 0.2 = -0.282842712 n + 0.2 = -0.282842712 Reorder the terms: 0.2 + n = -0.282842712 Solving 0.2 + n = -0.282842712 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + n = -0.282842712 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + n = -0.282842712 + -0.2 n = -0.282842712 + -0.2 Combine like terms: -0.282842712 + -0.2 = -0.482842712 n = -0.482842712 Simplifying n = -0.482842712Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.082842712, -0.482842712}
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