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Simplifying n2 = 10n + 5 Reorder the terms: n2 = 5 + 10n Solving n2 = 5 + 10n Solving for variable 'n'. Reorder the terms: -5 + -10n + n2 = 5 + 10n + -5 + -10n Reorder the terms: -5 + -10n + n2 = 5 + -5 + 10n + -10n Combine like terms: 5 + -5 = 0 -5 + -10n + n2 = 0 + 10n + -10n -5 + -10n + n2 = 10n + -10n Combine like terms: 10n + -10n = 0 -5 + -10n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -10n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -10n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -10n + n2 = 0 + 5 -10n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -10n + n2 = 5 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 = 5 + 25 Reorder the terms: 25 + -10n + n2 = 5 + 25 Combine like terms: 5 + 25 = 30 25 + -10n + n2 = 30 Factor a perfect square on the left side: (n + -5)(n + -5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (n + -5) equal to 5.477225575 and -5.477225575.Subproblem 1
n + -5 = 5.477225575 Simplifying n + -5 = 5.477225575 Reorder the terms: -5 + n = 5.477225575 Solving -5 + n = 5.477225575 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 = 5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + n = 5.477225575 + 5 n = 5.477225575 + 5 Combine like terms: 5.477225575 + 5 = 10.477225575 n = 10.477225575 Simplifying n = 10.477225575Subproblem 2
n + -5 = -5.477225575 Simplifying n + -5 = -5.477225575 Reorder the terms: -5 + n = -5.477225575 Solving -5 + n = -5.477225575 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 = -5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + n = -5.477225575 + 5 n = -5.477225575 + 5 Combine like terms: -5.477225575 + 5 = -0.477225575 n = -0.477225575 Simplifying n = -0.477225575Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.477225575, -0.477225575}
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