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Simplifying n2 + 3n + -2 = 0 Reorder the terms: -2 + 3n + n2 = 0 Solving -2 + 3n + 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 + 3n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + 3n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3n + n2 = 0 + 2 3n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 3n + n2 = 2 The n term is 3n. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3n + 2.25 + n2 = 2 + 2.25 Reorder the terms: 2.25 + 3n + n2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3n + n2 = 4.25 Factor a perfect square on the left side: (n + 1.5)(n + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (n + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
n + 1.5 = 2.061552813 Simplifying n + 1.5 = 2.061552813 Reorder the terms: 1.5 + n = 2.061552813 Solving 1.5 + n = 2.061552813 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 2.061552813 + -1.5 n = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 n = 0.561552813 Simplifying n = 0.561552813Subproblem 2
n + 1.5 = -2.061552813 Simplifying n + 1.5 = -2.061552813 Reorder the terms: 1.5 + n = -2.061552813 Solving 1.5 + n = -2.061552813 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -2.061552813 + -1.5 n = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 n = -3.561552813 Simplifying n = -3.561552813Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.561552813, -3.561552813}
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