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Simplifying 5n2 + -44n = 6n + -21 Reorder the terms: -44n + 5n2 = 6n + -21 Reorder the terms: -44n + 5n2 = -21 + 6n Solving -44n + 5n2 = -21 + 6n Solving for variable 'n'. Reorder the terms: 21 + -44n + -6n + 5n2 = -21 + 6n + 21 + -6n Combine like terms: -44n + -6n = -50n 21 + -50n + 5n2 = -21 + 6n + 21 + -6n Reorder the terms: 21 + -50n + 5n2 = -21 + 21 + 6n + -6n Combine like terms: -21 + 21 = 0 21 + -50n + 5n2 = 0 + 6n + -6n 21 + -50n + 5n2 = 6n + -6n Combine like terms: 6n + -6n = 0 21 + -50n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.2 + -10n + n2 = 0 Move the constant term to the right: Add '-4.2' to each side of the equation. 4.2 + -10n + -4.2 + n2 = 0 + -4.2 Reorder the terms: 4.2 + -4.2 + -10n + n2 = 0 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + -10n + n2 = 0 + -4.2 -10n + n2 = 0 + -4.2 Combine like terms: 0 + -4.2 = -4.2 -10n + n2 = -4.2 The n term is -10n. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10n + 25 + n2 = -4.2 + 25 Reorder the terms: 25 + -10n + n2 = -4.2 + 25 Combine like terms: -4.2 + 25 = 20.8 25 + -10n + n2 = 20.8 Factor a perfect square on the left side: (n + -5)(n + -5) = 20.8 Calculate the square root of the right side: 4.5607017 Break this problem into two subproblems by setting (n + -5) equal to 4.5607017 and -4.5607017.Subproblem 1
n + -5 = 4.5607017 Simplifying n + -5 = 4.5607017 Reorder the terms: -5 + n = 4.5607017 Solving -5 + n = 4.5607017 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 4.5607017 + 5 Combine like terms: -5 + 5 = 0 0 + n = 4.5607017 + 5 n = 4.5607017 + 5 Combine like terms: 4.5607017 + 5 = 9.5607017 n = 9.5607017 Simplifying n = 9.5607017Subproblem 2
n + -5 = -4.5607017 Simplifying n + -5 = -4.5607017 Reorder the terms: -5 + n = -4.5607017 Solving -5 + n = -4.5607017 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = -4.5607017 + 5 Combine like terms: -5 + 5 = 0 0 + n = -4.5607017 + 5 n = -4.5607017 + 5 Combine like terms: -4.5607017 + 5 = 0.4392983 n = 0.4392983 Simplifying n = 0.4392983Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.5607017, 0.4392983}
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