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Simplifying n2 + -10n + -5 = -8 Reorder the terms: -5 + -10n + n2 = -8 Solving -5 + -10n + n2 = -8 Solving for variable 'n'. Reorder the terms: -5 + 8 + -10n + n2 = -8 + 8 Combine like terms: -5 + 8 = 3 3 + -10n + n2 = -8 + 8 Combine like terms: -8 + 8 = 0 3 + -10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + -10n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10n + n2 = 0 + -3 -10n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10n + n2 = -3 The n term is -10n. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10n + 25 + n2 = -3 + 25 Reorder the terms: 25 + -10n + n2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + -10n + n2 = 22 Factor a perfect square on the left side: (n + -5)(n + -5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (n + -5) equal to 4.69041576 and -4.69041576.Subproblem 1
n + -5 = 4.69041576 Simplifying n + -5 = 4.69041576 Reorder the terms: -5 + n = 4.69041576 Solving -5 + n = 4.69041576 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + n = 4.69041576 + 5 n = 4.69041576 + 5 Combine like terms: 4.69041576 + 5 = 9.69041576 n = 9.69041576 Simplifying n = 9.69041576Subproblem 2
n + -5 = -4.69041576 Simplifying n + -5 = -4.69041576 Reorder the terms: -5 + n = -4.69041576 Solving -5 + n = -4.69041576 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = -4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + n = -4.69041576 + 5 n = -4.69041576 + 5 Combine like terms: -4.69041576 + 5 = 0.30958424 n = 0.30958424 Simplifying n = 0.30958424Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.69041576, 0.30958424}
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