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Simplifying (n + 4)(n + -5) = 26 Reorder the terms: (4 + n)(n + -5) = 26 Reorder the terms: (4 + n)(-5 + n) = 26 Multiply (4 + n) * (-5 + n) (4(-5 + n) + n(-5 + n)) = 26 ((-5 * 4 + n * 4) + n(-5 + n)) = 26 ((-20 + 4n) + n(-5 + n)) = 26 (-20 + 4n + (-5 * n + n * n)) = 26 (-20 + 4n + (-5n + n2)) = 26 Combine like terms: 4n + -5n = -1n (-20 + -1n + n2) = 26 Solving -20 + -1n + n2 = 26 Solving for variable 'n'. Reorder the terms: -20 + -26 + -1n + n2 = 26 + -26 Combine like terms: -20 + -26 = -46 -46 + -1n + n2 = 26 + -26 Combine like terms: 26 + -26 = 0 -46 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -1n + 46 + n2 = 0 + 46 Reorder the terms: -46 + 46 + -1n + n2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -1n + n2 = 0 + 46 -1n + n2 = 0 + 46 Combine like terms: 0 + 46 = 46 -1n + n2 = 46 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 = 46 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 46 + 0.25 Combine like terms: 46 + 0.25 = 46.25 0.25 + -1n + n2 = 46.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (n + -0.5) equal to 6.800735254 and -6.800735254.Subproblem 1
n + -0.5 = 6.800735254 Simplifying n + -0.5 = 6.800735254 Reorder the terms: -0.5 + n = 6.800735254 Solving -0.5 + n = 6.800735254 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 = 6.800735254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 6.800735254 + 0.5 n = 6.800735254 + 0.5 Combine like terms: 6.800735254 + 0.5 = 7.300735254 n = 7.300735254 Simplifying n = 7.300735254Subproblem 2
n + -0.5 = -6.800735254 Simplifying n + -0.5 = -6.800735254 Reorder the terms: -0.5 + n = -6.800735254 Solving -0.5 + n = -6.800735254 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 = -6.800735254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -6.800735254 + 0.5 n = -6.800735254 + 0.5 Combine like terms: -6.800735254 + 0.5 = -6.300735254 n = -6.300735254 Simplifying n = -6.300735254Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.300735254, -6.300735254}
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