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Simplifying n2 + -5n + -9 = 0 Reorder the terms: -9 + -5n + n2 = 0 Solving -9 + -5n + 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 + -5n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + -5n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5n + n2 = 0 + 9 -5n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 -5n + n2 = 9 The n term is -5n. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5n + 6.25 + n2 = 9 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 9 + 6.25 Combine like terms: 9 + 6.25 = 15.25 6.25 + -5n + n2 = 15.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (n + -2.5) equal to 3.905124838 and -3.905124838.Subproblem 1
n + -2.5 = 3.905124838 Simplifying n + -2.5 = 3.905124838 Reorder the terms: -2.5 + n = 3.905124838 Solving -2.5 + n = 3.905124838 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = 3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 3.905124838 + 2.5 n = 3.905124838 + 2.5 Combine like terms: 3.905124838 + 2.5 = 6.405124838 n = 6.405124838 Simplifying n = 6.405124838Subproblem 2
n + -2.5 = -3.905124838 Simplifying n + -2.5 = -3.905124838 Reorder the terms: -2.5 + n = -3.905124838 Solving -2.5 + n = -3.905124838 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + n = -3.905124838 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -3.905124838 + 2.5 n = -3.905124838 + 2.5 Combine like terms: -3.905124838 + 2.5 = -1.405124838 n = -1.405124838 Simplifying n = -1.405124838Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.405124838, -1.405124838}
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