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Simplifying n2 + 0.5n + -437 = 0 Reorder the terms: -437 + 0.5n + n2 = 0 Solving -437 + 0.5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '437' to each side of the equation. -437 + 0.5n + 437 + n2 = 0 + 437 Reorder the terms: -437 + 437 + 0.5n + n2 = 0 + 437 Combine like terms: -437 + 437 = 0 0 + 0.5n + n2 = 0 + 437 0.5n + n2 = 0 + 437 Combine like terms: 0 + 437 = 437 0.5n + n2 = 437 The n term is 0.5n. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5n + 0.0625 + n2 = 437 + 0.0625 Reorder the terms: 0.0625 + 0.5n + n2 = 437 + 0.0625 Combine like terms: 437 + 0.0625 = 437.0625 0.0625 + 0.5n + n2 = 437.0625 Factor a perfect square on the left side: (n + 0.25)(n + 0.25) = 437.0625 Calculate the square root of the right side: 20.906039797 Break this problem into two subproblems by setting (n + 0.25) equal to 20.906039797 and -20.906039797.Subproblem 1
n + 0.25 = 20.906039797 Simplifying n + 0.25 = 20.906039797 Reorder the terms: 0.25 + n = 20.906039797 Solving 0.25 + n = 20.906039797 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + n = 20.906039797 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + n = 20.906039797 + -0.25 n = 20.906039797 + -0.25 Combine like terms: 20.906039797 + -0.25 = 20.656039797 n = 20.656039797 Simplifying n = 20.656039797Subproblem 2
n + 0.25 = -20.906039797 Simplifying n + 0.25 = -20.906039797 Reorder the terms: 0.25 + n = -20.906039797 Solving 0.25 + n = -20.906039797 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + n = -20.906039797 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + n = -20.906039797 + -0.25 n = -20.906039797 + -0.25 Combine like terms: -20.906039797 + -0.25 = -21.156039797 n = -21.156039797 Simplifying n = -21.156039797Solution
The solution to the problem is based on the solutions from the subproblems. n = {20.656039797, -21.156039797}
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