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Simplifying (n + 2)((n + 2) + -9) = 18 Reorder the terms: (2 + n)((n + 2) + -9) = 18 Reorder the terms: (2 + n)((2 + n) + -9) = 18 Remove parenthesis around (2 + n) (2 + n)(2 + n + -9) = 18 Reorder the terms: (2 + n)(2 + -9 + n) = 18 Combine like terms: 2 + -9 = -7 (2 + n)(-7 + n) = 18 Multiply (2 + n) * (-7 + n) (2(-7 + n) + n(-7 + n)) = 18 ((-7 * 2 + n * 2) + n(-7 + n)) = 18 ((-14 + 2n) + n(-7 + n)) = 18 (-14 + 2n + (-7 * n + n * n)) = 18 (-14 + 2n + (-7n + n2)) = 18 Combine like terms: 2n + -7n = -5n (-14 + -5n + n2) = 18 Solving -14 + -5n + n2 = 18 Solving for variable 'n'. Reorder the terms: -14 + -18 + -5n + n2 = 18 + -18 Combine like terms: -14 + -18 = -32 -32 + -5n + n2 = 18 + -18 Combine like terms: 18 + -18 = 0 -32 + -5n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -5n + 32 + n2 = 0 + 32 Reorder the terms: -32 + 32 + -5n + n2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -5n + n2 = 0 + 32 -5n + n2 = 0 + 32 Combine like terms: 0 + 32 = 32 -5n + n2 = 32 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 = 32 + 6.25 Reorder the terms: 6.25 + -5n + n2 = 32 + 6.25 Combine like terms: 32 + 6.25 = 38.25 6.25 + -5n + n2 = 38.25 Factor a perfect square on the left side: (n + -2.5)(n + -2.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (n + -2.5) equal to 6.184658438 and -6.184658438.Subproblem 1
n + -2.5 = 6.184658438 Simplifying n + -2.5 = 6.184658438 Reorder the terms: -2.5 + n = 6.184658438 Solving -2.5 + n = 6.184658438 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 = 6.184658438 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = 6.184658438 + 2.5 n = 6.184658438 + 2.5 Combine like terms: 6.184658438 + 2.5 = 8.684658438 n = 8.684658438 Simplifying n = 8.684658438Subproblem 2
n + -2.5 = -6.184658438 Simplifying n + -2.5 = -6.184658438 Reorder the terms: -2.5 + n = -6.184658438 Solving -2.5 + n = -6.184658438 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 = -6.184658438 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + n = -6.184658438 + 2.5 n = -6.184658438 + 2.5 Combine like terms: -6.184658438 + 2.5 = -3.684658438 n = -3.684658438 Simplifying n = -3.684658438Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.684658438, -3.684658438}
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