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Simplifying n2 + -10n = 7 Reorder the terms: -10n + n2 = 7 Solving -10n + n2 = 7 Solving for variable 'n'. Reorder the terms: -7 + -10n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -10n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + -10n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10n + n2 = 0 + 7 -10n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 -10n + n2 = 7 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 = 7 + 25 Reorder the terms: 25 + -10n + n2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + -10n + n2 = 32 Factor a perfect square on the left side: (n + -5)(n + -5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (n + -5) equal to 5.656854249 and -5.656854249.Subproblem 1
n + -5 = 5.656854249 Simplifying n + -5 = 5.656854249 Reorder the terms: -5 + n = 5.656854249 Solving -5 + n = 5.656854249 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 = 5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + n = 5.656854249 + 5 n = 5.656854249 + 5 Combine like terms: 5.656854249 + 5 = 10.656854249 n = 10.656854249 Simplifying n = 10.656854249Subproblem 2
n + -5 = -5.656854249 Simplifying n + -5 = -5.656854249 Reorder the terms: -5 + n = -5.656854249 Solving -5 + n = -5.656854249 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 = -5.656854249 + 5 Combine like terms: -5 + 5 = 0 0 + n = -5.656854249 + 5 n = -5.656854249 + 5 Combine like terms: -5.656854249 + 5 = -0.656854249 n = -0.656854249 Simplifying n = -0.656854249Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.656854249, -0.656854249}
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