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Simplifying (n + 1)(n + -2) = 3 Reorder the terms: (1 + n)(n + -2) = 3 Reorder the terms: (1 + n)(-2 + n) = 3 Multiply (1 + n) * (-2 + n) (1(-2 + n) + n(-2 + n)) = 3 ((-2 * 1 + n * 1) + n(-2 + n)) = 3 ((-2 + 1n) + n(-2 + n)) = 3 (-2 + 1n + (-2 * n + n * n)) = 3 (-2 + 1n + (-2n + n2)) = 3 Combine like terms: 1n + -2n = -1n (-2 + -1n + n2) = 3 Solving -2 + -1n + n2 = 3 Solving for variable 'n'. Reorder the terms: -2 + -3 + -1n + n2 = 3 + -3 Combine like terms: -2 + -3 = -5 -5 + -1n + n2 = 3 + -3 Combine like terms: 3 + -3 = 0 -5 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -1n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -1n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1n + n2 = 0 + 5 -1n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1n + n2 = 5 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 5 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1n + n2 = 5.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (n + -0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
n + -0.5 = 2.291287847 Simplifying n + -0.5 = 2.291287847 Reorder the terms: -0.5 + n = 2.291287847 Solving -0.5 + n = 2.291287847 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 2.291287847 + 0.5 n = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 n = 2.791287847 Simplifying n = 2.791287847Subproblem 2
n + -0.5 = -2.291287847 Simplifying n + -0.5 = -2.291287847 Reorder the terms: -0.5 + n = -2.291287847 Solving -0.5 + n = -2.291287847 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -2.291287847 + 0.5 n = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 n = -1.791287847 Simplifying n = -1.791287847Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.791287847, -1.791287847}
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