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Simplifying n2 + 10n + -2 = -8 Reorder the terms: -2 + 10n + n2 = -8 Solving -2 + 10n + n2 = -8 Solving for variable 'n'. Reorder the terms: -2 + 8 + 10n + n2 = -8 + 8 Combine like terms: -2 + 8 = 6 6 + 10n + n2 = -8 + 8 Combine like terms: -8 + 8 = 0 6 + 10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 10n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + 10n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 10n + n2 = 0 + -6 10n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 10n + n2 = -6 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 = -6 + 25 Reorder the terms: 25 + 10n + n2 = -6 + 25 Combine like terms: -6 + 25 = 19 25 + 10n + n2 = 19 Factor a perfect square on the left side: (n + 5)(n + 5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (n + 5) equal to 4.358898944 and -4.358898944.Subproblem 1
n + 5 = 4.358898944 Simplifying n + 5 = 4.358898944 Reorder the terms: 5 + n = 4.358898944 Solving 5 + n = 4.358898944 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 = 4.358898944 + -5 Combine like terms: 5 + -5 = 0 0 + n = 4.358898944 + -5 n = 4.358898944 + -5 Combine like terms: 4.358898944 + -5 = -0.641101056 n = -0.641101056 Simplifying n = -0.641101056Subproblem 2
n + 5 = -4.358898944 Simplifying n + 5 = -4.358898944 Reorder the terms: 5 + n = -4.358898944 Solving 5 + n = -4.358898944 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 = -4.358898944 + -5 Combine like terms: 5 + -5 = 0 0 + n = -4.358898944 + -5 n = -4.358898944 + -5 Combine like terms: -4.358898944 + -5 = -9.358898944 n = -9.358898944 Simplifying n = -9.358898944Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.641101056, -9.358898944}
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