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Simplifying n2 + 20n + 14 = -7 Reorder the terms: 14 + 20n + n2 = -7 Solving 14 + 20n + n2 = -7 Solving for variable 'n'. Reorder the terms: 14 + 7 + 20n + n2 = -7 + 7 Combine like terms: 14 + 7 = 21 21 + 20n + n2 = -7 + 7 Combine like terms: -7 + 7 = 0 21 + 20n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 20n + -21 + n2 = 0 + -21 Reorder the terms: 21 + -21 + 20n + n2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 20n + n2 = 0 + -21 20n + n2 = 0 + -21 Combine like terms: 0 + -21 = -21 20n + n2 = -21 The n term is 20n. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20n + 100 + n2 = -21 + 100 Reorder the terms: 100 + 20n + n2 = -21 + 100 Combine like terms: -21 + 100 = 79 100 + 20n + n2 = 79 Factor a perfect square on the left side: (n + 10)(n + 10) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (n + 10) equal to 8.888194417 and -8.888194417.Subproblem 1
n + 10 = 8.888194417 Simplifying n + 10 = 8.888194417 Reorder the terms: 10 + n = 8.888194417 Solving 10 + n = 8.888194417 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 8.888194417 + -10 Combine like terms: 10 + -10 = 0 0 + n = 8.888194417 + -10 n = 8.888194417 + -10 Combine like terms: 8.888194417 + -10 = -1.111805583 n = -1.111805583 Simplifying n = -1.111805583Subproblem 2
n + 10 = -8.888194417 Simplifying n + 10 = -8.888194417 Reorder the terms: 10 + n = -8.888194417 Solving 10 + n = -8.888194417 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = -8.888194417 + -10 Combine like terms: 10 + -10 = 0 0 + n = -8.888194417 + -10 n = -8.888194417 + -10 Combine like terms: -8.888194417 + -10 = -18.888194417 n = -18.888194417 Simplifying n = -18.888194417Solution
The solution to the problem is based on the solutions from the subproblems. n = {-1.111805583, -18.888194417}
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