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Simplifying n2 + 19n + -2000 = 0 Reorder the terms: -2000 + 19n + n2 = 0 Solving -2000 + 19n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 19n + 2000 + n2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 19n + n2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 19n + n2 = 0 + 2000 19n + n2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 19n + n2 = 2000 The n term is 19n. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19n + 90.25 + n2 = 2000 + 90.25 Reorder the terms: 90.25 + 19n + n2 = 2000 + 90.25 Combine like terms: 2000 + 90.25 = 2090.25 90.25 + 19n + n2 = 2090.25 Factor a perfect square on the left side: (n + 9.5)(n + 9.5) = 2090.25 Calculate the square root of the right side: 45.719251962 Break this problem into two subproblems by setting (n + 9.5) equal to 45.719251962 and -45.719251962.Subproblem 1
n + 9.5 = 45.719251962 Simplifying n + 9.5 = 45.719251962 Reorder the terms: 9.5 + n = 45.719251962 Solving 9.5 + n = 45.719251962 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + n = 45.719251962 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + n = 45.719251962 + -9.5 n = 45.719251962 + -9.5 Combine like terms: 45.719251962 + -9.5 = 36.219251962 n = 36.219251962 Simplifying n = 36.219251962Subproblem 2
n + 9.5 = -45.719251962 Simplifying n + 9.5 = -45.719251962 Reorder the terms: 9.5 + n = -45.719251962 Solving 9.5 + n = -45.719251962 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + n = -45.719251962 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + n = -45.719251962 + -9.5 n = -45.719251962 + -9.5 Combine like terms: -45.719251962 + -9.5 = -55.219251962 n = -55.219251962 Simplifying n = -55.219251962Solution
The solution to the problem is based on the solutions from the subproblems. n = {36.219251962, -55.219251962}
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