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Simplifying 4n2 + -11n + -29 = -5 Reorder the terms: -29 + -11n + 4n2 = -5 Solving -29 + -11n + 4n2 = -5 Solving for variable 'n'. Reorder the terms: -29 + 5 + -11n + 4n2 = -5 + 5 Combine like terms: -29 + 5 = -24 -24 + -11n + 4n2 = -5 + 5 Combine like terms: -5 + 5 = 0 -24 + -11n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6 + -2.75n + n2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.75n + 6 + n2 = 0 + 6 Reorder the terms: -6 + 6 + -2.75n + n2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.75n + n2 = 0 + 6 -2.75n + n2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.75n + n2 = 6 The n term is -2.75n. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75n + 1.890625 + n2 = 6 + 1.890625 Reorder the terms: 1.890625 + -2.75n + n2 = 6 + 1.890625 Combine like terms: 6 + 1.890625 = 7.890625 1.890625 + -2.75n + n2 = 7.890625 Factor a perfect square on the left side: (n + -1.375)(n + -1.375) = 7.890625 Calculate the square root of the right side: 2.809025632 Break this problem into two subproblems by setting (n + -1.375) equal to 2.809025632 and -2.809025632.Subproblem 1
n + -1.375 = 2.809025632 Simplifying n + -1.375 = 2.809025632 Reorder the terms: -1.375 + n = 2.809025632 Solving -1.375 + n = 2.809025632 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + n = 2.809025632 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + n = 2.809025632 + 1.375 n = 2.809025632 + 1.375 Combine like terms: 2.809025632 + 1.375 = 4.184025632 n = 4.184025632 Simplifying n = 4.184025632Subproblem 2
n + -1.375 = -2.809025632 Simplifying n + -1.375 = -2.809025632 Reorder the terms: -1.375 + n = -2.809025632 Solving -1.375 + n = -2.809025632 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + n = -2.809025632 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + n = -2.809025632 + 1.375 n = -2.809025632 + 1.375 Combine like terms: -2.809025632 + 1.375 = -1.434025632 n = -1.434025632 Simplifying n = -1.434025632Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.184025632, -1.434025632}
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