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Simplifying n2 + -5n + 2 = 0 Reorder the terms: 2 + -5n + n2 = 0 Solving 2 + -5n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + -5n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5n + n2 = 0 + -2 -5n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5n + n2 = -2 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 = -2 + 6.25 Reorder the terms: 6.25 + -5n + n2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + -5n + n2 = 4.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (n + -2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
n + -2.5 = 2.061552813 Simplifying n + -2.5 = 2.061552813 Reorder the terms: -2.5 + n = 2.061552813 Solving -2.5 + n = 2.061552813 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 = 2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 2.061552813 + 2.5 n = 2.061552813 + 2.5 Combine like terms: 2.061552813 + 2.5 = 4.561552813 n = 4.561552813 Simplifying n = 4.561552813Subproblem 2
n + -2.5 = -2.061552813 Simplifying n + -2.5 = -2.061552813 Reorder the terms: -2.5 + n = -2.061552813 Solving -2.5 + n = -2.061552813 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 = -2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -2.061552813 + 2.5 n = -2.061552813 + 2.5 Combine like terms: -2.061552813 + 2.5 = 0.438447187 n = 0.438447187 Simplifying n = 0.438447187Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.561552813, 0.438447187}
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