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Simplifying n2 + -11n + 3 = 5 Reorder the terms: 3 + -11n + n2 = 5 Solving 3 + -11n + n2 = 5 Solving for variable 'n'. Reorder the terms: 3 + -5 + -11n + n2 = 5 + -5 Combine like terms: 3 + -5 = -2 -2 + -11n + n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -2 + -11n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -11n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + -11n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -11n + n2 = 0 + 2 -11n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 -11n + n2 = 2 The n term is -11n. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11n + 30.25 + n2 = 2 + 30.25 Reorder the terms: 30.25 + -11n + n2 = 2 + 30.25 Combine like terms: 2 + 30.25 = 32.25 30.25 + -11n + n2 = 32.25 Factor a perfect square on the left side: (n + -5.5)(n + -5.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (n + -5.5) equal to 5.678908346 and -5.678908346.Subproblem 1
n + -5.5 = 5.678908346 Simplifying n + -5.5 = 5.678908346 Reorder the terms: -5.5 + n = 5.678908346 Solving -5.5 + n = 5.678908346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 5.678908346 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 5.678908346 + 5.5 n = 5.678908346 + 5.5 Combine like terms: 5.678908346 + 5.5 = 11.178908346 n = 11.178908346 Simplifying n = 11.178908346Subproblem 2
n + -5.5 = -5.678908346 Simplifying n + -5.5 = -5.678908346 Reorder the terms: -5.5 + n = -5.678908346 Solving -5.5 + n = -5.678908346 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -5.678908346 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -5.678908346 + 5.5 n = -5.678908346 + 5.5 Combine like terms: -5.678908346 + 5.5 = -0.178908346 n = -0.178908346 Simplifying n = -0.178908346Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.178908346, -0.178908346}
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