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Simplifying 0.1n2 + -20n + -5100 = 0 Reorder the terms: -5100 + -20n + 0.1n2 = 0 Solving -5100 + -20n + 0.1n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -51000 + -200n + n2 = 0 Move the constant term to the right: Add '51000' to each side of the equation. -51000 + -200n + 51000 + n2 = 0 + 51000 Reorder the terms: -51000 + 51000 + -200n + n2 = 0 + 51000 Combine like terms: -51000 + 51000 = 0 0 + -200n + n2 = 0 + 51000 -200n + n2 = 0 + 51000 Combine like terms: 0 + 51000 = 51000 -200n + n2 = 51000 The n term is -200n. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200n + 10000 + n2 = 51000 + 10000 Reorder the terms: 10000 + -200n + n2 = 51000 + 10000 Combine like terms: 51000 + 10000 = 61000 10000 + -200n + n2 = 61000 Factor a perfect square on the left side: (n + -100)(n + -100) = 61000 Calculate the square root of the right side: 246.981780705 Break this problem into two subproblems by setting (n + -100) equal to 246.981780705 and -246.981780705.Subproblem 1
n + -100 = 246.981780705 Simplifying n + -100 = 246.981780705 Reorder the terms: -100 + n = 246.981780705 Solving -100 + n = 246.981780705 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + n = 246.981780705 + 100 Combine like terms: -100 + 100 = 0 0 + n = 246.981780705 + 100 n = 246.981780705 + 100 Combine like terms: 246.981780705 + 100 = 346.981780705 n = 346.981780705 Simplifying n = 346.981780705Subproblem 2
n + -100 = -246.981780705 Simplifying n + -100 = -246.981780705 Reorder the terms: -100 + n = -246.981780705 Solving -100 + n = -246.981780705 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + n = -246.981780705 + 100 Combine like terms: -100 + 100 = 0 0 + n = -246.981780705 + 100 n = -246.981780705 + 100 Combine like terms: -246.981780705 + 100 = -146.981780705 n = -146.981780705 Simplifying n = -146.981780705Solution
The solution to the problem is based on the solutions from the subproblems. n = {346.981780705, -146.981780705}
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