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Simplifying -1n2 + 6n + 19 = 2 Reorder the terms: 19 + 6n + -1n2 = 2 Solving 19 + 6n + -1n2 = 2 Solving for variable 'n'. Reorder the terms: 19 + -2 + 6n + -1n2 = 2 + -2 Combine like terms: 19 + -2 = 17 17 + 6n + -1n2 = 2 + -2 Combine like terms: 2 + -2 = 0 17 + 6n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + -6n + n2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + -6n + 17 + n2 = 0 + 17 Reorder the terms: -17 + 17 + -6n + n2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -6n + n2 = 0 + 17 -6n + n2 = 0 + 17 Combine like terms: 0 + 17 = 17 -6n + n2 = 17 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 17 + 9 Reorder the terms: 9 + -6n + n2 = 17 + 9 Combine like terms: 17 + 9 = 26 9 + -6n + n2 = 26 Factor a perfect square on the left side: (n + -3)(n + -3) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (n + -3) equal to 5.099019514 and -5.099019514.Subproblem 1
n + -3 = 5.099019514 Simplifying n + -3 = 5.099019514 Reorder the terms: -3 + n = 5.099019514 Solving -3 + n = 5.099019514 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 5.099019514 + 3 Combine like terms: -3 + 3 = 0 0 + n = 5.099019514 + 3 n = 5.099019514 + 3 Combine like terms: 5.099019514 + 3 = 8.099019514 n = 8.099019514 Simplifying n = 8.099019514Subproblem 2
n + -3 = -5.099019514 Simplifying n + -3 = -5.099019514 Reorder the terms: -3 + n = -5.099019514 Solving -3 + n = -5.099019514 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -5.099019514 + 3 Combine like terms: -3 + 3 = 0 0 + n = -5.099019514 + 3 n = -5.099019514 + 3 Combine like terms: -5.099019514 + 3 = -2.099019514 n = -2.099019514 Simplifying n = -2.099019514Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.099019514, -2.099019514}
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