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Simplifying n2 + -9 = 2n + 9 Reorder the terms: -9 + n2 = 2n + 9 Reorder the terms: -9 + n2 = 9 + 2n Solving -9 + n2 = 9 + 2n Solving for variable 'n'. Reorder the terms: -9 + -9 + -2n + n2 = 9 + 2n + -9 + -2n Combine like terms: -9 + -9 = -18 -18 + -2n + n2 = 9 + 2n + -9 + -2n Reorder the terms: -18 + -2n + n2 = 9 + -9 + 2n + -2n Combine like terms: 9 + -9 = 0 -18 + -2n + n2 = 0 + 2n + -2n -18 + -2n + n2 = 2n + -2n Combine like terms: 2n + -2n = 0 -18 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -2n + 18 + n2 = 0 + 18 Reorder the terms: -18 + 18 + -2n + n2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2n + n2 = 0 + 18 -2n + n2 = 0 + 18 Combine like terms: 0 + 18 = 18 -2n + n2 = 18 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 18 + 1 Reorder the terms: 1 + -2n + n2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + -2n + n2 = 19 Factor a perfect square on the left side: (n + -1)(n + -1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (n + -1) equal to 4.358898944 and -4.358898944.Subproblem 1
n + -1 = 4.358898944 Simplifying n + -1 = 4.358898944 Reorder the terms: -1 + n = 4.358898944 Solving -1 + n = 4.358898944 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + n = 4.358898944 + 1 n = 4.358898944 + 1 Combine like terms: 4.358898944 + 1 = 5.358898944 n = 5.358898944 Simplifying n = 5.358898944Subproblem 2
n + -1 = -4.358898944 Simplifying n + -1 = -4.358898944 Reorder the terms: -1 + n = -4.358898944 Solving -1 + n = -4.358898944 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + n = -4.358898944 + 1 n = -4.358898944 + 1 Combine like terms: -4.358898944 + 1 = -3.358898944 n = -3.358898944 Simplifying n = -3.358898944Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.358898944, -3.358898944}
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