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Simplifying n2 + -10n + -13 = 0 Reorder the terms: -13 + -10n + n2 = 0 Solving -13 + -10n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -10n + 13 + n2 = 0 + 13 Reorder the terms: -13 + 13 + -10n + n2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -10n + n2 = 0 + 13 -10n + n2 = 0 + 13 Combine like terms: 0 + 13 = 13 -10n + n2 = 13 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 = 13 + 25 Reorder the terms: 25 + -10n + n2 = 13 + 25 Combine like terms: 13 + 25 = 38 25 + -10n + n2 = 38 Factor a perfect square on the left side: (n + -5)(n + -5) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (n + -5) equal to 6.164414003 and -6.164414003.Subproblem 1
n + -5 = 6.164414003 Simplifying n + -5 = 6.164414003 Reorder the terms: -5 + n = 6.164414003 Solving -5 + n = 6.164414003 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 = 6.164414003 + 5 Combine like terms: -5 + 5 = 0 0 + n = 6.164414003 + 5 n = 6.164414003 + 5 Combine like terms: 6.164414003 + 5 = 11.164414003 n = 11.164414003 Simplifying n = 11.164414003Subproblem 2
n + -5 = -6.164414003 Simplifying n + -5 = -6.164414003 Reorder the terms: -5 + n = -6.164414003 Solving -5 + n = -6.164414003 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 = -6.164414003 + 5 Combine like terms: -5 + 5 = 0 0 + n = -6.164414003 + 5 n = -6.164414003 + 5 Combine like terms: -6.164414003 + 5 = -1.164414003 n = -1.164414003 Simplifying n = -1.164414003Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.164414003, -1.164414003}
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