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Simplifying n(n) + -40n + -399 = 0 Multiply n * n n2 + -40n + -399 = 0 Reorder the terms: -399 + -40n + n2 = 0 Solving -399 + -40n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '399' to each side of the equation. -399 + -40n + 399 + n2 = 0 + 399 Reorder the terms: -399 + 399 + -40n + n2 = 0 + 399 Combine like terms: -399 + 399 = 0 0 + -40n + n2 = 0 + 399 -40n + n2 = 0 + 399 Combine like terms: 0 + 399 = 399 -40n + n2 = 399 The n term is -40n. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40n + 400 + n2 = 399 + 400 Reorder the terms: 400 + -40n + n2 = 399 + 400 Combine like terms: 399 + 400 = 799 400 + -40n + n2 = 799 Factor a perfect square on the left side: (n + -20)(n + -20) = 799 Calculate the square root of the right side: 28.26658805 Break this problem into two subproblems by setting (n + -20) equal to 28.26658805 and -28.26658805.Subproblem 1
n + -20 = 28.26658805 Simplifying n + -20 = 28.26658805 Reorder the terms: -20 + n = 28.26658805 Solving -20 + n = 28.26658805 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + n = 28.26658805 + 20 Combine like terms: -20 + 20 = 0 0 + n = 28.26658805 + 20 n = 28.26658805 + 20 Combine like terms: 28.26658805 + 20 = 48.26658805 n = 48.26658805 Simplifying n = 48.26658805Subproblem 2
n + -20 = -28.26658805 Simplifying n + -20 = -28.26658805 Reorder the terms: -20 + n = -28.26658805 Solving -20 + n = -28.26658805 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + n = -28.26658805 + 20 Combine like terms: -20 + 20 = 0 0 + n = -28.26658805 + 20 n = -28.26658805 + 20 Combine like terms: -28.26658805 + 20 = -8.26658805 n = -8.26658805 Simplifying n = -8.26658805Solution
The solution to the problem is based on the solutions from the subproblems. n = {48.26658805, -8.26658805}
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