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Simplifying n2 + 2n + -9.2416 = 0 Reorder the terms: -9.2416 + 2n + n2 = 0 Solving -9.2416 + 2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '9.2416' to each side of the equation. -9.2416 + 2n + 9.2416 + n2 = 0 + 9.2416 Reorder the terms: -9.2416 + 9.2416 + 2n + n2 = 0 + 9.2416 Combine like terms: -9.2416 + 9.2416 = 0.0000 0.0000 + 2n + n2 = 0 + 9.2416 2n + n2 = 0 + 9.2416 Combine like terms: 0 + 9.2416 = 9.2416 2n + n2 = 9.2416 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 = 9.2416 + 1 Reorder the terms: 1 + 2n + n2 = 9.2416 + 1 Combine like terms: 9.2416 + 1 = 10.2416 1 + 2n + n2 = 10.2416 Factor a perfect square on the left side: (n + 1)(n + 1) = 10.2416 Calculate the square root of the right side: 3.20024999 Break this problem into two subproblems by setting (n + 1) equal to 3.20024999 and -3.20024999.Subproblem 1
n + 1 = 3.20024999 Simplifying n + 1 = 3.20024999 Reorder the terms: 1 + n = 3.20024999 Solving 1 + n = 3.20024999 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 = 3.20024999 + -1 Combine like terms: 1 + -1 = 0 0 + n = 3.20024999 + -1 n = 3.20024999 + -1 Combine like terms: 3.20024999 + -1 = 2.20024999 n = 2.20024999 Simplifying n = 2.20024999Subproblem 2
n + 1 = -3.20024999 Simplifying n + 1 = -3.20024999 Reorder the terms: 1 + n = -3.20024999 Solving 1 + n = -3.20024999 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 = -3.20024999 + -1 Combine like terms: 1 + -1 = 0 0 + n = -3.20024999 + -1 n = -3.20024999 + -1 Combine like terms: -3.20024999 + -1 = -4.20024999 n = -4.20024999 Simplifying n = -4.20024999Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.20024999, -4.20024999}
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