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Simplifying 2n2 + -4n + -26 = -5 Reorder the terms: -26 + -4n + 2n2 = -5 Solving -26 + -4n + 2n2 = -5 Solving for variable 'n'. Reorder the terms: -26 + 5 + -4n + 2n2 = -5 + 5 Combine like terms: -26 + 5 = -21 -21 + -4n + 2n2 = -5 + 5 Combine like terms: -5 + 5 = 0 -21 + -4n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -2n + n2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -2n + 10.5 + n2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -2n + n2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -2n + n2 = 0 + 10.5 -2n + n2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -2n + n2 = 10.5 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 10.5 + 1 Reorder the terms: 1 + -2n + n2 = 10.5 + 1 Combine like terms: 10.5 + 1 = 11.5 1 + -2n + n2 = 11.5 Factor a perfect square on the left side: (n + -1)(n + -1) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (n + -1) equal to 3.391164992 and -3.391164992.Subproblem 1
n + -1 = 3.391164992 Simplifying n + -1 = 3.391164992 Reorder the terms: -1 + n = 3.391164992 Solving -1 + n = 3.391164992 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 3.391164992 + 1 Combine like terms: -1 + 1 = 0 0 + n = 3.391164992 + 1 n = 3.391164992 + 1 Combine like terms: 3.391164992 + 1 = 4.391164992 n = 4.391164992 Simplifying n = 4.391164992Subproblem 2
n + -1 = -3.391164992 Simplifying n + -1 = -3.391164992 Reorder the terms: -1 + n = -3.391164992 Solving -1 + n = -3.391164992 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -3.391164992 + 1 Combine like terms: -1 + 1 = 0 0 + n = -3.391164992 + 1 n = -3.391164992 + 1 Combine like terms: -3.391164992 + 1 = -2.391164992 n = -2.391164992 Simplifying n = -2.391164992Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.391164992, -2.391164992}
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