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Simplifying 5n2 + 117n + 72 = 0 Reorder the terms: 72 + 117n + 5n2 = 0 Solving 72 + 117n + 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 + 23.4n + n2 = 0 Move the constant term to the right: Add '-14.4' to each side of the equation. 14.4 + 23.4n + -14.4 + n2 = 0 + -14.4 Reorder the terms: 14.4 + -14.4 + 23.4n + n2 = 0 + -14.4 Combine like terms: 14.4 + -14.4 = 0.0 0.0 + 23.4n + n2 = 0 + -14.4 23.4n + n2 = 0 + -14.4 Combine like terms: 0 + -14.4 = -14.4 23.4n + n2 = -14.4 The n term is 23.4n. Take half its coefficient (11.7). Square it (136.89) and add it to both sides. Add '136.89' to each side of the equation. 23.4n + 136.89 + n2 = -14.4 + 136.89 Reorder the terms: 136.89 + 23.4n + n2 = -14.4 + 136.89 Combine like terms: -14.4 + 136.89 = 122.49 136.89 + 23.4n + n2 = 122.49 Factor a perfect square on the left side: (n + 11.7)(n + 11.7) = 122.49 Calculate the square root of the right side: 11.067520047 Break this problem into two subproblems by setting (n + 11.7) equal to 11.067520047 and -11.067520047.Subproblem 1
n + 11.7 = 11.067520047 Simplifying n + 11.7 = 11.067520047 Reorder the terms: 11.7 + n = 11.067520047 Solving 11.7 + n = 11.067520047 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-11.7' to each side of the equation. 11.7 + -11.7 + n = 11.067520047 + -11.7 Combine like terms: 11.7 + -11.7 = 0.0 0.0 + n = 11.067520047 + -11.7 n = 11.067520047 + -11.7 Combine like terms: 11.067520047 + -11.7 = -0.632479953 n = -0.632479953 Simplifying n = -0.632479953Subproblem 2
n + 11.7 = -11.067520047 Simplifying n + 11.7 = -11.067520047 Reorder the terms: 11.7 + n = -11.067520047 Solving 11.7 + n = -11.067520047 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-11.7' to each side of the equation. 11.7 + -11.7 + n = -11.067520047 + -11.7 Combine like terms: 11.7 + -11.7 = 0.0 0.0 + n = -11.067520047 + -11.7 n = -11.067520047 + -11.7 Combine like terms: -11.067520047 + -11.7 = -22.767520047 n = -22.767520047 Simplifying n = -22.767520047Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.632479953, -22.767520047}
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