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Simplifying -9n2 + -10n = -5 Reorder the terms: -10n + -9n2 = -5 Solving -10n + -9n2 = -5 Solving for variable 'n'. Reorder the terms: 5 + -10n + -9n2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -10n + -9n2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.5555555556 + 1.111111111n + n2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 1.111111111n + 0.5555555556 + n2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 1.111111111n + n2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 1.111111111n + n2 = 0 + 0.5555555556 1.111111111n + n2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 1.111111111n + n2 = 0.5555555556 The n term is 1.111111111n. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111n + 0.3086419752 + n2 = 0.5555555556 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111n + n2 = 0.5555555556 + 0.3086419752 Combine like terms: 0.5555555556 + 0.3086419752 = 0.8641975308 0.3086419752 + 1.111111111n + n2 = 0.8641975308 Factor a perfect square on the left side: (n + 0.5555555555)(n + 0.5555555555) = 0.8641975308 Calculate the square root of the right side: 0.929622252 Break this problem into two subproblems by setting (n + 0.5555555555) equal to 0.929622252 and -0.929622252.Subproblem 1
n + 0.5555555555 = 0.929622252 Simplifying n + 0.5555555555 = 0.929622252 Reorder the terms: 0.5555555555 + n = 0.929622252 Solving 0.5555555555 + n = 0.929622252 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + n = 0.929622252 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + n = 0.929622252 + -0.5555555555 n = 0.929622252 + -0.5555555555 Combine like terms: 0.929622252 + -0.5555555555 = 0.3740666965 n = 0.3740666965 Simplifying n = 0.3740666965Subproblem 2
n + 0.5555555555 = -0.929622252 Simplifying n + 0.5555555555 = -0.929622252 Reorder the terms: 0.5555555555 + n = -0.929622252 Solving 0.5555555555 + n = -0.929622252 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + n = -0.929622252 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + n = -0.929622252 + -0.5555555555 n = -0.929622252 + -0.5555555555 Combine like terms: -0.929622252 + -0.5555555555 = -1.4851778075 n = -1.4851778075 Simplifying n = -1.4851778075Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.3740666965, -1.4851778075}
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