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Simplifying (n * n) + 20n + -440 = 0 Multiply n * n (n2) + 20n + -440 = 0 n2 + 20n + -440 = 0 Reorder the terms: -440 + 20n + n2 = 0 Solving -440 + 20n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '440' to each side of the equation. -440 + 20n + 440 + n2 = 0 + 440 Reorder the terms: -440 + 440 + 20n + n2 = 0 + 440 Combine like terms: -440 + 440 = 0 0 + 20n + n2 = 0 + 440 20n + n2 = 0 + 440 Combine like terms: 0 + 440 = 440 20n + n2 = 440 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 = 440 + 100 Reorder the terms: 100 + 20n + n2 = 440 + 100 Combine like terms: 440 + 100 = 540 100 + 20n + n2 = 540 Factor a perfect square on the left side: (n + 10)(n + 10) = 540 Calculate the square root of the right side: 23.237900077 Break this problem into two subproblems by setting (n + 10) equal to 23.237900077 and -23.237900077.Subproblem 1
n + 10 = 23.237900077 Simplifying n + 10 = 23.237900077 Reorder the terms: 10 + n = 23.237900077 Solving 10 + n = 23.237900077 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 = 23.237900077 + -10 Combine like terms: 10 + -10 = 0 0 + n = 23.237900077 + -10 n = 23.237900077 + -10 Combine like terms: 23.237900077 + -10 = 13.237900077 n = 13.237900077 Simplifying n = 13.237900077Subproblem 2
n + 10 = -23.237900077 Simplifying n + 10 = -23.237900077 Reorder the terms: 10 + n = -23.237900077 Solving 10 + n = -23.237900077 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 = -23.237900077 + -10 Combine like terms: 10 + -10 = 0 0 + n = -23.237900077 + -10 n = -23.237900077 + -10 Combine like terms: -23.237900077 + -10 = -33.237900077 n = -33.237900077 Simplifying n = -33.237900077Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.237900077, -33.237900077}
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