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Simplifying n2 + -22n + 121 = 13 Reorder the terms: 121 + -22n + n2 = 13 Solving 121 + -22n + n2 = 13 Solving for variable 'n'. Reorder the terms: 121 + -13 + -22n + n2 = 13 + -13 Combine like terms: 121 + -13 = 108 108 + -22n + n2 = 13 + -13 Combine like terms: 13 + -13 = 0 108 + -22n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-108' to each side of the equation. 108 + -22n + -108 + n2 = 0 + -108 Reorder the terms: 108 + -108 + -22n + n2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + -22n + n2 = 0 + -108 -22n + n2 = 0 + -108 Combine like terms: 0 + -108 = -108 -22n + n2 = -108 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 = -108 + 121 Reorder the terms: 121 + -22n + n2 = -108 + 121 Combine like terms: -108 + 121 = 13 121 + -22n + n2 = 13 Factor a perfect square on the left side: (n + -11)(n + -11) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (n + -11) equal to 3.605551275 and -3.605551275.Subproblem 1
n + -11 = 3.605551275 Simplifying n + -11 = 3.605551275 Reorder the terms: -11 + n = 3.605551275 Solving -11 + n = 3.605551275 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 = 3.605551275 + 11 Combine like terms: -11 + 11 = 0 0 + n = 3.605551275 + 11 n = 3.605551275 + 11 Combine like terms: 3.605551275 + 11 = 14.605551275 n = 14.605551275 Simplifying n = 14.605551275Subproblem 2
n + -11 = -3.605551275 Simplifying n + -11 = -3.605551275 Reorder the terms: -11 + n = -3.605551275 Solving -11 + n = -3.605551275 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 = -3.605551275 + 11 Combine like terms: -11 + 11 = 0 0 + n = -3.605551275 + 11 n = -3.605551275 + 11 Combine like terms: -3.605551275 + 11 = 7.394448725 n = 7.394448725 Simplifying n = 7.394448725Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.605551275, 7.394448725}
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