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Simplifying n2 + -3n + -44 = 0 Reorder the terms: -44 + -3n + n2 = 0 Solving -44 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -3n + 44 + n2 = 0 + 44 Reorder the terms: -44 + 44 + -3n + n2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -3n + n2 = 0 + 44 -3n + n2 = 0 + 44 Combine like terms: 0 + 44 = 44 -3n + n2 = 44 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 44 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 44 + 2.25 Combine like terms: 44 + 2.25 = 46.25 2.25 + -3n + n2 = 46.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (n + -1.5) equal to 6.800735254 and -6.800735254.Subproblem 1
n + -1.5 = 6.800735254 Simplifying n + -1.5 = 6.800735254 Reorder the terms: -1.5 + n = 6.800735254 Solving -1.5 + n = 6.800735254 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 6.800735254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 6.800735254 + 1.5 n = 6.800735254 + 1.5 Combine like terms: 6.800735254 + 1.5 = 8.300735254 n = 8.300735254 Simplifying n = 8.300735254Subproblem 2
n + -1.5 = -6.800735254 Simplifying n + -1.5 = -6.800735254 Reorder the terms: -1.5 + n = -6.800735254 Solving -1.5 + n = -6.800735254 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -6.800735254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -6.800735254 + 1.5 n = -6.800735254 + 1.5 Combine like terms: -6.800735254 + 1.5 = -5.300735254 n = -5.300735254 Simplifying n = -5.300735254Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.300735254, -5.300735254}
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