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Simplifying n2 + 20n = -94 Reorder the terms: 20n + n2 = -94 Solving 20n + n2 = -94 Solving for variable 'n'. Reorder the terms: 94 + 20n + n2 = -94 + 94 Combine like terms: -94 + 94 = 0 94 + 20n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-94' to each side of the equation. 94 + 20n + -94 + n2 = 0 + -94 Reorder the terms: 94 + -94 + 20n + n2 = 0 + -94 Combine like terms: 94 + -94 = 0 0 + 20n + n2 = 0 + -94 20n + n2 = 0 + -94 Combine like terms: 0 + -94 = -94 20n + n2 = -94 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 = -94 + 100 Reorder the terms: 100 + 20n + n2 = -94 + 100 Combine like terms: -94 + 100 = 6 100 + 20n + n2 = 6 Factor a perfect square on the left side: (n + 10)(n + 10) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (n + 10) equal to 2.449489743 and -2.449489743.Subproblem 1
n + 10 = 2.449489743 Simplifying n + 10 = 2.449489743 Reorder the terms: 10 + n = 2.449489743 Solving 10 + n = 2.449489743 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 = 2.449489743 + -10 Combine like terms: 10 + -10 = 0 0 + n = 2.449489743 + -10 n = 2.449489743 + -10 Combine like terms: 2.449489743 + -10 = -7.550510257 n = -7.550510257 Simplifying n = -7.550510257Subproblem 2
n + 10 = -2.449489743 Simplifying n + 10 = -2.449489743 Reorder the terms: 10 + n = -2.449489743 Solving 10 + n = -2.449489743 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 = -2.449489743 + -10 Combine like terms: 10 + -10 = 0 0 + n = -2.449489743 + -10 n = -2.449489743 + -10 Combine like terms: -2.449489743 + -10 = -12.449489743 n = -12.449489743 Simplifying n = -12.449489743Solution
The solution to the problem is based on the solutions from the subproblems. n = {-7.550510257, -12.449489743}
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