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Simplifying n2 + -15n = 2000 Reorder the terms: -15n + n2 = 2000 Solving -15n + n2 = 2000 Solving for variable 'n'. Reorder the terms: -2000 + -15n + n2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -2000 + -15n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + -15n + 2000 + n2 = 0 + 2000 Reorder the terms: -2000 + 2000 + -15n + n2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + -15n + n2 = 0 + 2000 -15n + n2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 -15n + n2 = 2000 The n term is -15n. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15n + 56.25 + n2 = 2000 + 56.25 Reorder the terms: 56.25 + -15n + n2 = 2000 + 56.25 Combine like terms: 2000 + 56.25 = 2056.25 56.25 + -15n + n2 = 2056.25 Factor a perfect square on the left side: (n + -7.5)(n + -7.5) = 2056.25 Calculate the square root of the right side: 45.345892868 Break this problem into two subproblems by setting (n + -7.5) equal to 45.345892868 and -45.345892868.Subproblem 1
n + -7.5 = 45.345892868 Simplifying n + -7.5 = 45.345892868 Reorder the terms: -7.5 + n = 45.345892868 Solving -7.5 + n = 45.345892868 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = 45.345892868 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = 45.345892868 + 7.5 n = 45.345892868 + 7.5 Combine like terms: 45.345892868 + 7.5 = 52.845892868 n = 52.845892868 Simplifying n = 52.845892868Subproblem 2
n + -7.5 = -45.345892868 Simplifying n + -7.5 = -45.345892868 Reorder the terms: -7.5 + n = -45.345892868 Solving -7.5 + n = -45.345892868 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = -45.345892868 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = -45.345892868 + 7.5 n = -45.345892868 + 7.5 Combine like terms: -45.345892868 + 7.5 = -37.845892868 n = -37.845892868 Simplifying n = -37.845892868Solution
The solution to the problem is based on the solutions from the subproblems. n = {52.845892868, -37.845892868}
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