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Simplifying 5n2 + 27n = 28 Reorder the terms: 27n + 5n2 = 28 Solving 27n + 5n2 = 28 Solving for variable 'n'. Reorder the terms: -28 + 27n + 5n2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 27n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + 5.4n + n2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 5.4n + 5.6 + n2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 5.4n + n2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 5.4n + n2 = 0 + 5.6 5.4n + n2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 5.4n + n2 = 5.6 The n term is 5.4n. Take half its coefficient (2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. 5.4n + 7.29 + n2 = 5.6 + 7.29 Reorder the terms: 7.29 + 5.4n + n2 = 5.6 + 7.29 Combine like terms: 5.6 + 7.29 = 12.89 7.29 + 5.4n + n2 = 12.89 Factor a perfect square on the left side: (n + 2.7)(n + 2.7) = 12.89 Calculate the square root of the right side: 3.590264614 Break this problem into two subproblems by setting (n + 2.7) equal to 3.590264614 and -3.590264614.Subproblem 1
n + 2.7 = 3.590264614 Simplifying n + 2.7 = 3.590264614 Reorder the terms: 2.7 + n = 3.590264614 Solving 2.7 + n = 3.590264614 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + n = 3.590264614 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + n = 3.590264614 + -2.7 n = 3.590264614 + -2.7 Combine like terms: 3.590264614 + -2.7 = 0.890264614 n = 0.890264614 Simplifying n = 0.890264614Subproblem 2
n + 2.7 = -3.590264614 Simplifying n + 2.7 = -3.590264614 Reorder the terms: 2.7 + n = -3.590264614 Solving 2.7 + n = -3.590264614 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + n = -3.590264614 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + n = -3.590264614 + -2.7 n = -3.590264614 + -2.7 Combine like terms: -3.590264614 + -2.7 = -6.290264614 n = -6.290264614 Simplifying n = -6.290264614Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.890264614, -6.290264614}
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