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Simplifying n2 + -25n + -100 = 0 Reorder the terms: -100 + -25n + n2 = 0 Solving -100 + -25n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -25n + 100 + n2 = 0 + 100 Reorder the terms: -100 + 100 + -25n + n2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -25n + n2 = 0 + 100 -25n + n2 = 0 + 100 Combine like terms: 0 + 100 = 100 -25n + n2 = 100 The n term is -25n. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25n + 156.25 + n2 = 100 + 156.25 Reorder the terms: 156.25 + -25n + n2 = 100 + 156.25 Combine like terms: 100 + 156.25 = 256.25 156.25 + -25n + n2 = 256.25 Factor a perfect square on the left side: (n + -12.5)(n + -12.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (n + -12.5) equal to 16.007810594 and -16.007810594.Subproblem 1
n + -12.5 = 16.007810594 Simplifying n + -12.5 = 16.007810594 Reorder the terms: -12.5 + n = 16.007810594 Solving -12.5 + n = 16.007810594 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + n = 16.007810594 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + n = 16.007810594 + 12.5 n = 16.007810594 + 12.5 Combine like terms: 16.007810594 + 12.5 = 28.507810594 n = 28.507810594 Simplifying n = 28.507810594Subproblem 2
n + -12.5 = -16.007810594 Simplifying n + -12.5 = -16.007810594 Reorder the terms: -12.5 + n = -16.007810594 Solving -12.5 + n = -16.007810594 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + n = -16.007810594 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + n = -16.007810594 + 12.5 n = -16.007810594 + 12.5 Combine like terms: -16.007810594 + 12.5 = -3.507810594 n = -3.507810594 Simplifying n = -3.507810594Solution
The solution to the problem is based on the solutions from the subproblems. n = {28.507810594, -3.507810594}
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