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Simplifying n2 + -1n + -1460 = 0 Reorder the terms: -1460 + -1n + n2 = 0 Solving -1460 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '1460' to each side of the equation. -1460 + -1n + 1460 + n2 = 0 + 1460 Reorder the terms: -1460 + 1460 + -1n + n2 = 0 + 1460 Combine like terms: -1460 + 1460 = 0 0 + -1n + n2 = 0 + 1460 -1n + n2 = 0 + 1460 Combine like terms: 0 + 1460 = 1460 -1n + n2 = 1460 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 1460 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 1460 + 0.25 Combine like terms: 1460 + 0.25 = 1460.25 0.25 + -1n + n2 = 1460.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 1460.25 Calculate the square root of the right side: 38.213217609 Break this problem into two subproblems by setting (n + -0.5) equal to 38.213217609 and -38.213217609.Subproblem 1
n + -0.5 = 38.213217609 Simplifying n + -0.5 = 38.213217609 Reorder the terms: -0.5 + n = 38.213217609 Solving -0.5 + n = 38.213217609 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 38.213217609 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 38.213217609 + 0.5 n = 38.213217609 + 0.5 Combine like terms: 38.213217609 + 0.5 = 38.713217609 n = 38.713217609 Simplifying n = 38.713217609Subproblem 2
n + -0.5 = -38.213217609 Simplifying n + -0.5 = -38.213217609 Reorder the terms: -0.5 + n = -38.213217609 Solving -0.5 + n = -38.213217609 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -38.213217609 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -38.213217609 + 0.5 n = -38.213217609 + 0.5 Combine like terms: -38.213217609 + 0.5 = -37.713217609 n = -37.713217609 Simplifying n = -37.713217609Solution
The solution to the problem is based on the solutions from the subproblems. n = {38.713217609, -37.713217609}
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