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Simplifying (n + 3)(n + -2) = 88 Reorder the terms: (3 + n)(n + -2) = 88 Reorder the terms: (3 + n)(-2 + n) = 88 Multiply (3 + n) * (-2 + n) (3(-2 + n) + n(-2 + n)) = 88 ((-2 * 3 + n * 3) + n(-2 + n)) = 88 ((-6 + 3n) + n(-2 + n)) = 88 (-6 + 3n + (-2 * n + n * n)) = 88 (-6 + 3n + (-2n + n2)) = 88 Combine like terms: 3n + -2n = 1n (-6 + 1n + n2) = 88 Solving -6 + 1n + n2 = 88 Solving for variable 'n'. Reorder the terms: -6 + -88 + 1n + n2 = 88 + -88 Combine like terms: -6 + -88 = -94 -94 + 1n + n2 = 88 + -88 Combine like terms: 88 + -88 = 0 -94 + 1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + 1n + 94 + n2 = 0 + 94 Reorder the terms: -94 + 94 + 1n + n2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 1n + n2 = 0 + 94 1n + n2 = 0 + 94 Combine like terms: 0 + 94 = 94 1n + n2 = 94 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. n + 0.25 + n2 = 94 + 0.25 Reorder the terms: 0.25 + n + n2 = 94 + 0.25 Combine like terms: 94 + 0.25 = 94.25 0.25 + n + n2 = 94.25 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (n + 0.5) equal to 9.708243919 and -9.708243919.Subproblem 1
n + 0.5 = 9.708243919 Simplifying n + 0.5 = 9.708243919 Reorder the terms: 0.5 + n = 9.708243919 Solving 0.5 + n = 9.708243919 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 = 9.708243919 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 9.708243919 + -0.5 n = 9.708243919 + -0.5 Combine like terms: 9.708243919 + -0.5 = 9.208243919 n = 9.208243919 Simplifying n = 9.208243919Subproblem 2
n + 0.5 = -9.708243919 Simplifying n + 0.5 = -9.708243919 Reorder the terms: 0.5 + n = -9.708243919 Solving 0.5 + n = -9.708243919 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 = -9.708243919 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -9.708243919 + -0.5 n = -9.708243919 + -0.5 Combine like terms: -9.708243919 + -0.5 = -10.208243919 n = -10.208243919 Simplifying n = -10.208243919Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.208243919, -10.208243919}
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