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Simplifying n2 + 10n + -10 = 0 Reorder the terms: -10 + 10n + n2 = 0 Solving -10 + 10n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 10n + 10 + n2 = 0 + 10 Reorder the terms: -10 + 10 + 10n + n2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 10n + n2 = 0 + 10 10n + n2 = 0 + 10 Combine like terms: 0 + 10 = 10 10n + n2 = 10 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 = 10 + 25 Reorder the terms: 25 + 10n + n2 = 10 + 25 Combine like terms: 10 + 25 = 35 25 + 10n + n2 = 35 Factor a perfect square on the left side: (n + 5)(n + 5) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (n + 5) equal to 5.916079783 and -5.916079783.Subproblem 1
n + 5 = 5.916079783 Simplifying n + 5 = 5.916079783 Reorder the terms: 5 + n = 5.916079783 Solving 5 + n = 5.916079783 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 = 5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + n = 5.916079783 + -5 n = 5.916079783 + -5 Combine like terms: 5.916079783 + -5 = 0.916079783 n = 0.916079783 Simplifying n = 0.916079783Subproblem 2
n + 5 = -5.916079783 Simplifying n + 5 = -5.916079783 Reorder the terms: 5 + n = -5.916079783 Solving 5 + n = -5.916079783 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 = -5.916079783 + -5 Combine like terms: 5 + -5 = 0 0 + n = -5.916079783 + -5 n = -5.916079783 + -5 Combine like terms: -5.916079783 + -5 = -10.916079783 n = -10.916079783 Simplifying n = -10.916079783Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.916079783, -10.916079783}
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