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Simplifying n2 + 11n + 29 = 21 Reorder the terms: 29 + 11n + n2 = 21 Solving 29 + 11n + n2 = 21 Solving for variable 'n'. Reorder the terms: 29 + -21 + 11n + n2 = 21 + -21 Combine like terms: 29 + -21 = 8 8 + 11n + n2 = 21 + -21 Combine like terms: 21 + -21 = 0 8 + 11n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 11n + -8 + n2 = 0 + -8 Reorder the terms: 8 + -8 + 11n + n2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 11n + n2 = 0 + -8 11n + n2 = 0 + -8 Combine like terms: 0 + -8 = -8 11n + n2 = -8 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 = -8 + 30.25 Reorder the terms: 30.25 + 11n + n2 = -8 + 30.25 Combine like terms: -8 + 30.25 = 22.25 30.25 + 11n + n2 = 22.25 Factor a perfect square on the left side: (n + 5.5)(n + 5.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (n + 5.5) equal to 4.716990566 and -4.716990566.Subproblem 1
n + 5.5 = 4.716990566 Simplifying n + 5.5 = 4.716990566 Reorder the terms: 5.5 + n = 4.716990566 Solving 5.5 + n = 4.716990566 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 = 4.716990566 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + n = 4.716990566 + -5.5 n = 4.716990566 + -5.5 Combine like terms: 4.716990566 + -5.5 = -0.783009434 n = -0.783009434 Simplifying n = -0.783009434Subproblem 2
n + 5.5 = -4.716990566 Simplifying n + 5.5 = -4.716990566 Reorder the terms: 5.5 + n = -4.716990566 Solving 5.5 + n = -4.716990566 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 = -4.716990566 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + n = -4.716990566 + -5.5 n = -4.716990566 + -5.5 Combine like terms: -4.716990566 + -5.5 = -10.216990566 n = -10.216990566 Simplifying n = -10.216990566Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.783009434, -10.216990566}
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