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Simplifying n2 + -15n + -81 = 0 Reorder the terms: -81 + -15n + n2 = 0 Solving -81 + -15n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -15n + 81 + n2 = 0 + 81 Reorder the terms: -81 + 81 + -15n + n2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -15n + n2 = 0 + 81 -15n + n2 = 0 + 81 Combine like terms: 0 + 81 = 81 -15n + n2 = 81 The n term is -15n. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15n + 56.25 + n2 = 81 + 56.25 Reorder the terms: 56.25 + -15n + n2 = 81 + 56.25 Combine like terms: 81 + 56.25 = 137.25 56.25 + -15n + n2 = 137.25 Factor a perfect square on the left side: (n + -7.5)(n + -7.5) = 137.25 Calculate the square root of the right side: 11.715374514 Break this problem into two subproblems by setting (n + -7.5) equal to 11.715374514 and -11.715374514.Subproblem 1
n + -7.5 = 11.715374514 Simplifying n + -7.5 = 11.715374514 Reorder the terms: -7.5 + n = 11.715374514 Solving -7.5 + n = 11.715374514 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = 11.715374514 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = 11.715374514 + 7.5 n = 11.715374514 + 7.5 Combine like terms: 11.715374514 + 7.5 = 19.215374514 n = 19.215374514 Simplifying n = 19.215374514Subproblem 2
n + -7.5 = -11.715374514 Simplifying n + -7.5 = -11.715374514 Reorder the terms: -7.5 + n = -11.715374514 Solving -7.5 + n = -11.715374514 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + n = -11.715374514 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + n = -11.715374514 + 7.5 n = -11.715374514 + 7.5 Combine like terms: -11.715374514 + 7.5 = -4.215374514 n = -4.215374514 Simplifying n = -4.215374514Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.215374514, -4.215374514}
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