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Simplifying 0.25n + 0.05n(n + 5) = 2.95 Reorder the terms: 0.25n + 0.05n(5 + n) = 2.95 0.25n + (5 * 0.05n + n * 0.05n) = 2.95 0.25n + (0.25n + 0.05n2) = 2.95 Combine like terms: 0.25n + 0.25n = 0.5n 0.5n + 0.05n2 = 2.95 Solving 0.5n + 0.05n2 = 2.95 Solving for variable 'n'. Reorder the terms: -2.95 + 0.5n + 0.05n2 = 2.95 + -2.95 Combine like terms: 2.95 + -2.95 = 0.00 -2.95 + 0.5n + 0.05n2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -59 + 10n + n2 = 0 Move the constant term to the right: Add '59' to each side of the equation. -59 + 10n + 59 + n2 = 0 + 59 Reorder the terms: -59 + 59 + 10n + n2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 10n + n2 = 0 + 59 10n + n2 = 0 + 59 Combine like terms: 0 + 59 = 59 10n + n2 = 59 The n term is 10n. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10n + 25 + n2 = 59 + 25 Reorder the terms: 25 + 10n + n2 = 59 + 25 Combine like terms: 59 + 25 = 84 25 + 10n + n2 = 84 Factor a perfect square on the left side: (n + 5)(n + 5) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (n + 5) equal to 9.16515139 and -9.16515139.Subproblem 1
n + 5 = 9.16515139 Simplifying n + 5 = 9.16515139 Reorder the terms: 5 + n = 9.16515139 Solving 5 + n = 9.16515139 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 9.16515139 + -5 Combine like terms: 5 + -5 = 0 0 + n = 9.16515139 + -5 n = 9.16515139 + -5 Combine like terms: 9.16515139 + -5 = 4.16515139 n = 4.16515139 Simplifying n = 4.16515139Subproblem 2
n + 5 = -9.16515139 Simplifying n + 5 = -9.16515139 Reorder the terms: 5 + n = -9.16515139 Solving 5 + n = -9.16515139 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = -9.16515139 + -5 Combine like terms: 5 + -5 = 0 0 + n = -9.16515139 + -5 n = -9.16515139 + -5 Combine like terms: -9.16515139 + -5 = -14.16515139 n = -14.16515139 Simplifying n = -14.16515139Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.16515139, -14.16515139}
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