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Simplifying 5n2 + -33n + 24 = 0 Reorder the terms: 24 + -33n + 5n2 = 0 Solving 24 + -33n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.8 + -6.6n + n2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -6.6n + -4.8 + n2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -6.6n + n2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -6.6n + n2 = 0 + -4.8 -6.6n + n2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -6.6n + n2 = -4.8 The n term is -6.6n. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6n + 10.89 + n2 = -4.8 + 10.89 Reorder the terms: 10.89 + -6.6n + n2 = -4.8 + 10.89 Combine like terms: -4.8 + 10.89 = 6.09 10.89 + -6.6n + n2 = 6.09 Factor a perfect square on the left side: (n + -3.3)(n + -3.3) = 6.09 Calculate the square root of the right side: 2.467792536 Break this problem into two subproblems by setting (n + -3.3) equal to 2.467792536 and -2.467792536.Subproblem 1
n + -3.3 = 2.467792536 Simplifying n + -3.3 = 2.467792536 Reorder the terms: -3.3 + n = 2.467792536 Solving -3.3 + n = 2.467792536 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + n = 2.467792536 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + n = 2.467792536 + 3.3 n = 2.467792536 + 3.3 Combine like terms: 2.467792536 + 3.3 = 5.767792536 n = 5.767792536 Simplifying n = 5.767792536Subproblem 2
n + -3.3 = -2.467792536 Simplifying n + -3.3 = -2.467792536 Reorder the terms: -3.3 + n = -2.467792536 Solving -3.3 + n = -2.467792536 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + n = -2.467792536 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + n = -2.467792536 + 3.3 n = -2.467792536 + 3.3 Combine like terms: -2.467792536 + 3.3 = 0.832207464 n = 0.832207464 Simplifying n = 0.832207464Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.767792536, 0.832207464}
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