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Simplifying 27n2 + -5 + -6 = 4n Reorder the terms: -5 + -6 + 27n2 = 4n Combine like terms: -5 + -6 = -11 -11 + 27n2 = 4n Solving -11 + 27n2 = 4n Solving for variable 'n'. Reorder the terms: -11 + -4n + 27n2 = 4n + -4n Combine like terms: 4n + -4n = 0 -11 + -4n + 27n2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.4074074074 + -0.1481481481n + n2 = 0 Move the constant term to the right: Add '0.4074074074' to each side of the equation. -0.4074074074 + -0.1481481481n + 0.4074074074 + n2 = 0 + 0.4074074074 Reorder the terms: -0.4074074074 + 0.4074074074 + -0.1481481481n + n2 = 0 + 0.4074074074 Combine like terms: -0.4074074074 + 0.4074074074 = 0.0000000000 0.0000000000 + -0.1481481481n + n2 = 0 + 0.4074074074 -0.1481481481n + n2 = 0 + 0.4074074074 Combine like terms: 0 + 0.4074074074 = 0.4074074074 -0.1481481481n + n2 = 0.4074074074 The n term is -0.1481481481n. Take half its coefficient (-0.07407407405). Square it (0.005486968446) and add it to both sides. Add '0.005486968446' to each side of the equation. -0.1481481481n + 0.005486968446 + n2 = 0.4074074074 + 0.005486968446 Reorder the terms: 0.005486968446 + -0.1481481481n + n2 = 0.4074074074 + 0.005486968446 Combine like terms: 0.4074074074 + 0.005486968446 = 0.412894375846 0.005486968446 + -0.1481481481n + n2 = 0.412894375846 Factor a perfect square on the left side: (n + -0.07407407405)(n + -0.07407407405) = 0.412894375846 Calculate the square root of the right side: 0.642568577 Break this problem into two subproblems by setting (n + -0.07407407405) equal to 0.642568577 and -0.642568577.Subproblem 1
n + -0.07407407405 = 0.642568577 Simplifying n + -0.07407407405 = 0.642568577 Reorder the terms: -0.07407407405 + n = 0.642568577 Solving -0.07407407405 + n = 0.642568577 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.07407407405' to each side of the equation. -0.07407407405 + 0.07407407405 + n = 0.642568577 + 0.07407407405 Combine like terms: -0.07407407405 + 0.07407407405 = 0.00000000000 0.00000000000 + n = 0.642568577 + 0.07407407405 n = 0.642568577 + 0.07407407405 Combine like terms: 0.642568577 + 0.07407407405 = 0.71664265105 n = 0.71664265105 Simplifying n = 0.71664265105Subproblem 2
n + -0.07407407405 = -0.642568577 Simplifying n + -0.07407407405 = -0.642568577 Reorder the terms: -0.07407407405 + n = -0.642568577 Solving -0.07407407405 + n = -0.642568577 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.07407407405' to each side of the equation. -0.07407407405 + 0.07407407405 + n = -0.642568577 + 0.07407407405 Combine like terms: -0.07407407405 + 0.07407407405 = 0.00000000000 0.00000000000 + n = -0.642568577 + 0.07407407405 n = -0.642568577 + 0.07407407405 Combine like terms: -0.642568577 + 0.07407407405 = -0.56849450295 n = -0.56849450295 Simplifying n = -0.56849450295Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.71664265105, -0.56849450295}
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