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Simplifying n2 + -4 = 10n Reorder the terms: -4 + n2 = 10n Solving -4 + n2 = 10n Solving for variable 'n'. Reorder the terms: -4 + -10n + n2 = 10n + -10n Combine like terms: 10n + -10n = 0 -4 + -10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -10n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -10n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -10n + n2 = 0 + 4 -10n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -10n + n2 = 4 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 = 4 + 25 Reorder the terms: 25 + -10n + n2 = 4 + 25 Combine like terms: 4 + 25 = 29 25 + -10n + n2 = 29 Factor a perfect square on the left side: (n + -5)(n + -5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (n + -5) equal to 5.385164807 and -5.385164807.Subproblem 1
n + -5 = 5.385164807 Simplifying n + -5 = 5.385164807 Reorder the terms: -5 + n = 5.385164807 Solving -5 + n = 5.385164807 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 = 5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + n = 5.385164807 + 5 n = 5.385164807 + 5 Combine like terms: 5.385164807 + 5 = 10.385164807 n = 10.385164807 Simplifying n = 10.385164807Subproblem 2
n + -5 = -5.385164807 Simplifying n + -5 = -5.385164807 Reorder the terms: -5 + n = -5.385164807 Solving -5 + n = -5.385164807 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 = -5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + n = -5.385164807 + 5 n = -5.385164807 + 5 Combine like terms: -5.385164807 + 5 = -0.385164807 n = -0.385164807 Simplifying n = -0.385164807Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.385164807, -0.385164807}
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