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Simplifying n2 + -5n + -8 = 0 Reorder the terms: -8 + -5n + n2 = 0 Solving -8 + -5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -5n + 8 + n2 = 0 + 8 Reorder the terms: -8 + 8 + -5n + n2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5n + n2 = 0 + 8 -5n + n2 = 0 + 8 Combine like terms: 0 + 8 = 8 -5n + n2 = 8 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 = 8 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + -5n + n2 = 14.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (n + -2.5) equal to 3.774917218 and -3.774917218.Subproblem 1
n + -2.5 = 3.774917218 Simplifying n + -2.5 = 3.774917218 Reorder the terms: -2.5 + n = 3.774917218 Solving -2.5 + n = 3.774917218 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 = 3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 3.774917218 + 2.5 n = 3.774917218 + 2.5 Combine like terms: 3.774917218 + 2.5 = 6.274917218 n = 6.274917218 Simplifying n = 6.274917218Subproblem 2
n + -2.5 = -3.774917218 Simplifying n + -2.5 = -3.774917218 Reorder the terms: -2.5 + n = -3.774917218 Solving -2.5 + n = -3.774917218 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 = -3.774917218 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -3.774917218 + 2.5 n = -3.774917218 + 2.5 Combine like terms: -3.774917218 + 2.5 = -1.274917218 n = -1.274917218 Simplifying n = -1.274917218Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.274917218, -1.274917218}
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