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Simplifying n2 + -3n + -132 = 0 Reorder the terms: -132 + -3n + n2 = 0 Solving -132 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + -3n + 132 + n2 = 0 + 132 Reorder the terms: -132 + 132 + -3n + n2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + -3n + n2 = 0 + 132 -3n + n2 = 0 + 132 Combine like terms: 0 + 132 = 132 -3n + n2 = 132 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 132 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 132 + 2.25 Combine like terms: 132 + 2.25 = 134.25 2.25 + -3n + n2 = 134.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (n + -1.5) equal to 11.586630226 and -11.586630226.Subproblem 1
n + -1.5 = 11.586630226 Simplifying n + -1.5 = 11.586630226 Reorder the terms: -1.5 + n = 11.586630226 Solving -1.5 + n = 11.586630226 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 11.586630226 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 11.586630226 + 1.5 n = 11.586630226 + 1.5 Combine like terms: 11.586630226 + 1.5 = 13.086630226 n = 13.086630226 Simplifying n = 13.086630226Subproblem 2
n + -1.5 = -11.586630226 Simplifying n + -1.5 = -11.586630226 Reorder the terms: -1.5 + n = -11.586630226 Solving -1.5 + n = -11.586630226 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -11.586630226 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -11.586630226 + 1.5 n = -11.586630226 + 1.5 Combine like terms: -11.586630226 + 1.5 = -10.086630226 n = -10.086630226 Simplifying n = -10.086630226Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.086630226, -10.086630226}
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