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Simplifying 2925 = n(17.5 + 2.5n) 2925 = (17.5 * n + 2.5n * n) 2925 = (17.5n + 2.5n2) Solving 2925 = 17.5n + 2.5n2 Solving for variable 'n'. Reorder the terms: 2925 + -17.5n + -2.5n2 = 17.5n + -17.5n + 2.5n2 + -2.5n2 Combine like terms: 17.5n + -17.5n = 0.0 2925 + -17.5n + -2.5n2 = 0.0 + 2.5n2 + -2.5n2 2925 + -17.5n + -2.5n2 = 2.5n2 + -2.5n2 Combine like terms: 2.5n2 + -2.5n2 = 0.0 2925 + -17.5n + -2.5n2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -1170 + 7n + n2 = 0 Move the constant term to the right: Add '1170' to each side of the equation. -1170 + 7n + 1170 + n2 = 0 + 1170 Reorder the terms: -1170 + 1170 + 7n + n2 = 0 + 1170 Combine like terms: -1170 + 1170 = 0 0 + 7n + n2 = 0 + 1170 7n + n2 = 0 + 1170 Combine like terms: 0 + 1170 = 1170 7n + n2 = 1170 The n term is 7n. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7n + 12.25 + n2 = 1170 + 12.25 Reorder the terms: 12.25 + 7n + n2 = 1170 + 12.25 Combine like terms: 1170 + 12.25 = 1182.25 12.25 + 7n + n2 = 1182.25 Factor a perfect square on the left side: (n + 3.5)(n + 3.5) = 1182.25 Calculate the square root of the right side: 34.383862494 Break this problem into two subproblems by setting (n + 3.5) equal to 34.383862494 and -34.383862494.Subproblem 1
n + 3.5 = 34.383862494 Simplifying n + 3.5 = 34.383862494 Reorder the terms: 3.5 + n = 34.383862494 Solving 3.5 + n = 34.383862494 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = 34.383862494 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = 34.383862494 + -3.5 n = 34.383862494 + -3.5 Combine like terms: 34.383862494 + -3.5 = 30.883862494 n = 30.883862494 Simplifying n = 30.883862494Subproblem 2
n + 3.5 = -34.383862494 Simplifying n + 3.5 = -34.383862494 Reorder the terms: 3.5 + n = -34.383862494 Solving 3.5 + n = -34.383862494 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + n = -34.383862494 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + n = -34.383862494 + -3.5 n = -34.383862494 + -3.5 Combine like terms: -34.383862494 + -3.5 = -37.883862494 n = -37.883862494 Simplifying n = -37.883862494Solution
The solution to the problem is based on the solutions from the subproblems. n = {30.883862494, -37.883862494}
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