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Simplifying 13n2 + -27n + -6 = 0 Reorder the terms: -6 + -27n + 13n2 = 0 Solving -6 + -27n + 13n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.4615384615 + -2.076923077n + n2 = 0 Move the constant term to the right: Add '0.4615384615' to each side of the equation. -0.4615384615 + -2.076923077n + 0.4615384615 + n2 = 0 + 0.4615384615 Reorder the terms: -0.4615384615 + 0.4615384615 + -2.076923077n + n2 = 0 + 0.4615384615 Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000 0.0000000000 + -2.076923077n + n2 = 0 + 0.4615384615 -2.076923077n + n2 = 0 + 0.4615384615 Combine like terms: 0 + 0.4615384615 = 0.4615384615 -2.076923077n + n2 = 0.4615384615 The n term is -2.076923077n. Take half its coefficient (-1.038461539). Square it (1.078402368) and add it to both sides. Add '1.078402368' to each side of the equation. -2.076923077n + 1.078402368 + n2 = 0.4615384615 + 1.078402368 Reorder the terms: 1.078402368 + -2.076923077n + n2 = 0.4615384615 + 1.078402368 Combine like terms: 0.4615384615 + 1.078402368 = 1.5399408295 1.078402368 + -2.076923077n + n2 = 1.5399408295 Factor a perfect square on the left side: (n + -1.038461539)(n + -1.038461539) = 1.5399408295 Calculate the square root of the right side: 1.240943524 Break this problem into two subproblems by setting (n + -1.038461539) equal to 1.240943524 and -1.240943524.Subproblem 1
n + -1.038461539 = 1.240943524 Simplifying n + -1.038461539 = 1.240943524 Reorder the terms: -1.038461539 + n = 1.240943524 Solving -1.038461539 + n = 1.240943524 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.038461539' to each side of the equation. -1.038461539 + 1.038461539 + n = 1.240943524 + 1.038461539 Combine like terms: -1.038461539 + 1.038461539 = 0.000000000 0.000000000 + n = 1.240943524 + 1.038461539 n = 1.240943524 + 1.038461539 Combine like terms: 1.240943524 + 1.038461539 = 2.279405063 n = 2.279405063 Simplifying n = 2.279405063Subproblem 2
n + -1.038461539 = -1.240943524 Simplifying n + -1.038461539 = -1.240943524 Reorder the terms: -1.038461539 + n = -1.240943524 Solving -1.038461539 + n = -1.240943524 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.038461539' to each side of the equation. -1.038461539 + 1.038461539 + n = -1.240943524 + 1.038461539 Combine like terms: -1.038461539 + 1.038461539 = 0.000000000 0.000000000 + n = -1.240943524 + 1.038461539 n = -1.240943524 + 1.038461539 Combine like terms: -1.240943524 + 1.038461539 = -0.202481985 n = -0.202481985 Simplifying n = -0.202481985Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.279405063, -0.202481985}
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