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Simplifying (n + 1)(n + -5) = 36 Reorder the terms: (1 + n)(n + -5) = 36 Reorder the terms: (1 + n)(-5 + n) = 36 Multiply (1 + n) * (-5 + n) (1(-5 + n) + n(-5 + n)) = 36 ((-5 * 1 + n * 1) + n(-5 + n)) = 36 ((-5 + 1n) + n(-5 + n)) = 36 (-5 + 1n + (-5 * n + n * n)) = 36 (-5 + 1n + (-5n + n2)) = 36 Combine like terms: 1n + -5n = -4n (-5 + -4n + n2) = 36 Solving -5 + -4n + n2 = 36 Solving for variable 'n'. Reorder the terms: -5 + -36 + -4n + n2 = 36 + -36 Combine like terms: -5 + -36 = -41 -41 + -4n + n2 = 36 + -36 Combine like terms: 36 + -36 = 0 -41 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -4n + 41 + n2 = 0 + 41 Reorder the terms: -41 + 41 + -4n + n2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -4n + n2 = 0 + 41 -4n + n2 = 0 + 41 Combine like terms: 0 + 41 = 41 -4n + n2 = 41 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 41 + 4 Reorder the terms: 4 + -4n + n2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + -4n + n2 = 45 Factor a perfect square on the left side: (n + -2)(n + -2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (n + -2) equal to 6.708203933 and -6.708203933.Subproblem 1
n + -2 = 6.708203933 Simplifying n + -2 = 6.708203933 Reorder the terms: -2 + n = 6.708203933 Solving -2 + n = 6.708203933 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + n = 6.708203933 + 2 n = 6.708203933 + 2 Combine like terms: 6.708203933 + 2 = 8.708203933 n = 8.708203933 Simplifying n = 8.708203933Subproblem 2
n + -2 = -6.708203933 Simplifying n + -2 = -6.708203933 Reorder the terms: -2 + n = -6.708203933 Solving -2 + n = -6.708203933 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + n = -6.708203933 + 2 n = -6.708203933 + 2 Combine like terms: -6.708203933 + 2 = -4.708203933 n = -4.708203933 Simplifying n = -4.708203933Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.708203933, -4.708203933}
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