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Simplifying 0 = n2 + 11n + -28 Reorder the terms: 0 = -28 + 11n + n2 Solving 0 = -28 + 11n + n2 Solving for variable 'n'. Combine like terms: 0 + 28 = 28 28 + -11n + -1n2 = -28 + 11n + n2 + 28 + -11n + -1n2 Reorder the terms: 28 + -11n + -1n2 = -28 + 28 + 11n + -11n + n2 + -1n2 Combine like terms: -28 + 28 = 0 28 + -11n + -1n2 = 0 + 11n + -11n + n2 + -1n2 28 + -11n + -1n2 = 11n + -11n + n2 + -1n2 Combine like terms: 11n + -11n = 0 28 + -11n + -1n2 = 0 + n2 + -1n2 28 + -11n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 28 + -11n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + 11n + n2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 11n + 28 + n2 = 0 + 28 Reorder the terms: -28 + 28 + 11n + n2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 11n + n2 = 0 + 28 11n + n2 = 0 + 28 Combine like terms: 0 + 28 = 28 11n + n2 = 28 The n term is 11n. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11n + 30.25 + n2 = 28 + 30.25 Reorder the terms: 30.25 + 11n + n2 = 28 + 30.25 Combine like terms: 28 + 30.25 = 58.25 30.25 + 11n + n2 = 58.25 Factor a perfect square on the left side: (n + 5.5)(n + 5.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (n + 5.5) equal to 7.632168761 and -7.632168761.Subproblem 1
n + 5.5 = 7.632168761 Simplifying n + 5.5 = 7.632168761 Reorder the terms: 5.5 + n = 7.632168761 Solving 5.5 + n = 7.632168761 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + n = 7.632168761 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + n = 7.632168761 + -5.5 n = 7.632168761 + -5.5 Combine like terms: 7.632168761 + -5.5 = 2.132168761 n = 2.132168761 Simplifying n = 2.132168761Subproblem 2
n + 5.5 = -7.632168761 Simplifying n + 5.5 = -7.632168761 Reorder the terms: 5.5 + n = -7.632168761 Solving 5.5 + n = -7.632168761 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + n = -7.632168761 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + n = -7.632168761 + -5.5 n = -7.632168761 + -5.5 Combine like terms: -7.632168761 + -5.5 = -13.132168761 n = -13.132168761 Simplifying n = -13.132168761Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.132168761, -13.132168761}
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