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Simplifying n2 + n + -135 = 0 Reorder the terms: -135 + n + n2 = 0 Solving -135 + n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + n + 135 + n2 = 0 + 135 Reorder the terms: -135 + 135 + n + n2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + n + n2 = 0 + 135 n + n2 = 0 + 135 Combine like terms: 0 + 135 = 135 n + n2 = 135 The n term is n. 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. n + 0.25 + n2 = 135 + 0.25 Reorder the terms: 0.25 + n + n2 = 135 + 0.25 Combine like terms: 135 + 0.25 = 135.25 0.25 + n + n2 = 135.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 135.25 Calculate the square root of the right side: 11.62970335 Break this problem into two subproblems by setting (n + 0.5) equal to 11.62970335 and -11.62970335.Subproblem 1
n + 0.5 = 11.62970335 Simplifying n + 0.5 = 11.62970335 Reorder the terms: 0.5 + n = 11.62970335 Solving 0.5 + n = 11.62970335 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 = 11.62970335 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 11.62970335 + -0.5 n = 11.62970335 + -0.5 Combine like terms: 11.62970335 + -0.5 = 11.12970335 n = 11.12970335 Simplifying n = 11.12970335Subproblem 2
n + 0.5 = -11.62970335 Simplifying n + 0.5 = -11.62970335 Reorder the terms: 0.5 + n = -11.62970335 Solving 0.5 + n = -11.62970335 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 = -11.62970335 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -11.62970335 + -0.5 n = -11.62970335 + -0.5 Combine like terms: -11.62970335 + -0.5 = -12.12970335 n = -12.12970335 Simplifying n = -12.12970335Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.12970335, -12.12970335}
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