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Simplifying n2 + -22n + -9 = 0 Reorder the terms: -9 + -22n + n2 = 0 Solving -9 + -22n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -22n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + -22n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -22n + n2 = 0 + 9 -22n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 -22n + n2 = 9 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 = 9 + 121 Reorder the terms: 121 + -22n + n2 = 9 + 121 Combine like terms: 9 + 121 = 130 121 + -22n + n2 = 130 Factor a perfect square on the left side: (n + -11)(n + -11) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (n + -11) equal to 11.401754251 and -11.401754251.Subproblem 1
n + -11 = 11.401754251 Simplifying n + -11 = 11.401754251 Reorder the terms: -11 + n = 11.401754251 Solving -11 + n = 11.401754251 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 = 11.401754251 + 11 Combine like terms: -11 + 11 = 0 0 + n = 11.401754251 + 11 n = 11.401754251 + 11 Combine like terms: 11.401754251 + 11 = 22.401754251 n = 22.401754251 Simplifying n = 22.401754251Subproblem 2
n + -11 = -11.401754251 Simplifying n + -11 = -11.401754251 Reorder the terms: -11 + n = -11.401754251 Solving -11 + n = -11.401754251 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 = -11.401754251 + 11 Combine like terms: -11 + 11 = 0 0 + n = -11.401754251 + 11 n = -11.401754251 + 11 Combine like terms: -11.401754251 + 11 = -0.401754251 n = -0.401754251 Simplifying n = -0.401754251Solution
The solution to the problem is based on the solutions from the subproblems. n = {22.401754251, -0.401754251}
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