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Simplifying n2 + -1n + -2425 = 0 Reorder the terms: -2425 + -1n + n2 = 0 Solving -2425 + -1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2425' to each side of the equation. -2425 + -1n + 2425 + n2 = 0 + 2425 Reorder the terms: -2425 + 2425 + -1n + n2 = 0 + 2425 Combine like terms: -2425 + 2425 = 0 0 + -1n + n2 = 0 + 2425 -1n + n2 = 0 + 2425 Combine like terms: 0 + 2425 = 2425 -1n + n2 = 2425 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 = 2425 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 2425 + 0.25 Combine like terms: 2425 + 0.25 = 2425.25 0.25 + -1n + n2 = 2425.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 2425.25 Calculate the square root of the right side: 49.246827309 Break this problem into two subproblems by setting (n + -0.5) equal to 49.246827309 and -49.246827309.Subproblem 1
n + -0.5 = 49.246827309 Simplifying n + -0.5 = 49.246827309 Reorder the terms: -0.5 + n = 49.246827309 Solving -0.5 + n = 49.246827309 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 = 49.246827309 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 49.246827309 + 0.5 n = 49.246827309 + 0.5 Combine like terms: 49.246827309 + 0.5 = 49.746827309 n = 49.746827309 Simplifying n = 49.746827309Subproblem 2
n + -0.5 = -49.246827309 Simplifying n + -0.5 = -49.246827309 Reorder the terms: -0.5 + n = -49.246827309 Solving -0.5 + n = -49.246827309 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 = -49.246827309 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -49.246827309 + 0.5 n = -49.246827309 + 0.5 Combine like terms: -49.246827309 + 0.5 = -48.746827309 n = -48.746827309 Simplifying n = -48.746827309Solution
The solution to the problem is based on the solutions from the subproblems. n = {49.746827309, -48.746827309}
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