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Simplifying n2 + 22n + 35 = 0 Reorder the terms: 35 + 22n + n2 = 0 Solving 35 + 22n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 22n + -35 + n2 = 0 + -35 Reorder the terms: 35 + -35 + 22n + n2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 22n + n2 = 0 + -35 22n + n2 = 0 + -35 Combine like terms: 0 + -35 = -35 22n + n2 = -35 The n term is 22n. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22n + 121 + n2 = -35 + 121 Reorder the terms: 121 + 22n + n2 = -35 + 121 Combine like terms: -35 + 121 = 86 121 + 22n + n2 = 86 Factor a perfect square on the left side: (n + 11)(n + 11) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (n + 11) equal to 9.273618495 and -9.273618495.Subproblem 1
n + 11 = 9.273618495 Simplifying n + 11 = 9.273618495 Reorder the terms: 11 + n = 9.273618495 Solving 11 + n = 9.273618495 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + n = 9.273618495 + -11 Combine like terms: 11 + -11 = 0 0 + n = 9.273618495 + -11 n = 9.273618495 + -11 Combine like terms: 9.273618495 + -11 = -1.726381505 n = -1.726381505 Simplifying n = -1.726381505Subproblem 2
n + 11 = -9.273618495 Simplifying n + 11 = -9.273618495 Reorder the terms: 11 + n = -9.273618495 Solving 11 + n = -9.273618495 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + n = -9.273618495 + -11 Combine like terms: 11 + -11 = 0 0 + n = -9.273618495 + -11 n = -9.273618495 + -11 Combine like terms: -9.273618495 + -11 = -20.273618495 n = -20.273618495 Simplifying n = -20.273618495Solution
The solution to the problem is based on the solutions from the subproblems. n = {-1.726381505, -20.273618495}
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