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Simplifying (n + -3)(n + -4) = 49 Reorder the terms: (-3 + n)(n + -4) = 49 Reorder the terms: (-3 + n)(-4 + n) = 49 Multiply (-3 + n) * (-4 + n) (-3(-4 + n) + n(-4 + n)) = 49 ((-4 * -3 + n * -3) + n(-4 + n)) = 49 ((12 + -3n) + n(-4 + n)) = 49 (12 + -3n + (-4 * n + n * n)) = 49 (12 + -3n + (-4n + n2)) = 49 Combine like terms: -3n + -4n = -7n (12 + -7n + n2) = 49 Solving 12 + -7n + n2 = 49 Solving for variable 'n'. Reorder the terms: 12 + -49 + -7n + n2 = 49 + -49 Combine like terms: 12 + -49 = -37 -37 + -7n + n2 = 49 + -49 Combine like terms: 49 + -49 = 0 -37 + -7n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -7n + 37 + n2 = 0 + 37 Reorder the terms: -37 + 37 + -7n + n2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -7n + n2 = 0 + 37 -7n + n2 = 0 + 37 Combine like terms: 0 + 37 = 37 -7n + n2 = 37 The n term is -7n. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7n + 12.25 + n2 = 37 + 12.25 Reorder the terms: 12.25 + -7n + n2 = 37 + 12.25 Combine like terms: 37 + 12.25 = 49.25 12.25 + -7n + n2 = 49.25 Factor a perfect square on the left side: (n + -3.5)(n + -3.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (n + -3.5) equal to 7.017834424 and -7.017834424.Subproblem 1
n + -3.5 = 7.017834424 Simplifying n + -3.5 = 7.017834424 Reorder the terms: -3.5 + n = 7.017834424 Solving -3.5 + n = 7.017834424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = 7.017834424 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = 7.017834424 + 3.5 n = 7.017834424 + 3.5 Combine like terms: 7.017834424 + 3.5 = 10.517834424 n = 10.517834424 Simplifying n = 10.517834424Subproblem 2
n + -3.5 = -7.017834424 Simplifying n + -3.5 = -7.017834424 Reorder the terms: -3.5 + n = -7.017834424 Solving -3.5 + n = -7.017834424 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + n = -7.017834424 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + n = -7.017834424 + 3.5 n = -7.017834424 + 3.5 Combine like terms: -7.017834424 + 3.5 = -3.517834424 n = -3.517834424 Simplifying n = -3.517834424Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.517834424, -3.517834424}
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