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Simplifying n2 = 3n + 2 Reorder the terms: n2 = 2 + 3n Solving n2 = 2 + 3n Solving for variable 'n'. Reorder the terms: -2 + -3n + n2 = 2 + 3n + -2 + -3n Reorder the terms: -2 + -3n + n2 = 2 + -2 + 3n + -3n Combine like terms: 2 + -2 = 0 -2 + -3n + n2 = 0 + 3n + -3n -2 + -3n + n2 = 3n + -3n Combine like terms: 3n + -3n = 0 -2 + -3n + n2 = 0 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 = 3.561552813 n = 3.561552813 Simplifying n = 3.561552813Subproblem 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 = -0.561552813 n = -0.561552813 Simplifying n = -0.561552813Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.561552813, -0.561552813}
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