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Simplifying n2 + 10n + -80 = 0 Reorder the terms: -80 + 10n + n2 = 0 Solving -80 + 10n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 10n + 80 + n2 = 0 + 80 Reorder the terms: -80 + 80 + 10n + n2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 10n + n2 = 0 + 80 10n + n2 = 0 + 80 Combine like terms: 0 + 80 = 80 10n + n2 = 80 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 = 80 + 25 Reorder the terms: 25 + 10n + n2 = 80 + 25 Combine like terms: 80 + 25 = 105 25 + 10n + n2 = 105 Factor a perfect square on the left side: (n + 5)(n + 5) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (n + 5) equal to 10.246950766 and -10.246950766.Subproblem 1
n + 5 = 10.246950766 Simplifying n + 5 = 10.246950766 Reorder the terms: 5 + n = 10.246950766 Solving 5 + n = 10.246950766 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 = 10.246950766 + -5 Combine like terms: 5 + -5 = 0 0 + n = 10.246950766 + -5 n = 10.246950766 + -5 Combine like terms: 10.246950766 + -5 = 5.246950766 n = 5.246950766 Simplifying n = 5.246950766Subproblem 2
n + 5 = -10.246950766 Simplifying n + 5 = -10.246950766 Reorder the terms: 5 + n = -10.246950766 Solving 5 + n = -10.246950766 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 = -10.246950766 + -5 Combine like terms: 5 + -5 = 0 0 + n = -10.246950766 + -5 n = -10.246950766 + -5 Combine like terms: -10.246950766 + -5 = -15.246950766 n = -15.246950766 Simplifying n = -15.246950766Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.246950766, -15.246950766}
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