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Simplifying 5n2 + 107n + 72 = 0 Reorder the terms: 72 + 107n + 5n2 = 0 Solving 72 + 107n + 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'. 14.4 + 21.4n + n2 = 0 Move the constant term to the right: Add '-14.4' to each side of the equation. 14.4 + 21.4n + -14.4 + n2 = 0 + -14.4 Reorder the terms: 14.4 + -14.4 + 21.4n + n2 = 0 + -14.4 Combine like terms: 14.4 + -14.4 = 0.0 0.0 + 21.4n + n2 = 0 + -14.4 21.4n + n2 = 0 + -14.4 Combine like terms: 0 + -14.4 = -14.4 21.4n + n2 = -14.4 The n term is 21.4n. Take half its coefficient (10.7). Square it (114.49) and add it to both sides. Add '114.49' to each side of the equation. 21.4n + 114.49 + n2 = -14.4 + 114.49 Reorder the terms: 114.49 + 21.4n + n2 = -14.4 + 114.49 Combine like terms: -14.4 + 114.49 = 100.09 114.49 + 21.4n + n2 = 100.09 Factor a perfect square on the left side: (n + 10.7)(n + 10.7) = 100.09 Calculate the square root of the right side: 10.004498988 Break this problem into two subproblems by setting (n + 10.7) equal to 10.004498988 and -10.004498988.Subproblem 1
n + 10.7 = 10.004498988 Simplifying n + 10.7 = 10.004498988 Reorder the terms: 10.7 + n = 10.004498988 Solving 10.7 + n = 10.004498988 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10.7' to each side of the equation. 10.7 + -10.7 + n = 10.004498988 + -10.7 Combine like terms: 10.7 + -10.7 = 0.0 0.0 + n = 10.004498988 + -10.7 n = 10.004498988 + -10.7 Combine like terms: 10.004498988 + -10.7 = -0.695501012 n = -0.695501012 Simplifying n = -0.695501012Subproblem 2
n + 10.7 = -10.004498988 Simplifying n + 10.7 = -10.004498988 Reorder the terms: 10.7 + n = -10.004498988 Solving 10.7 + n = -10.004498988 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10.7' to each side of the equation. 10.7 + -10.7 + n = -10.004498988 + -10.7 Combine like terms: 10.7 + -10.7 = 0.0 0.0 + n = -10.004498988 + -10.7 n = -10.004498988 + -10.7 Combine like terms: -10.004498988 + -10.7 = -20.704498988 n = -20.704498988 Simplifying n = -20.704498988Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.695501012, -20.704498988}
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