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Simplifying 140n2 + 860n + -152000 = 0 Reorder the terms: -152000 + 860n + 140n2 = 0 Solving -152000 + 860n + 140n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '20'. 20(-7600 + 43n + 7n2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-7600 + 43n + 7n2)' equal to zero and attempt to solve: Simplifying -7600 + 43n + 7n2 = 0 Solving -7600 + 43n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1085.714286 + 6.142857143n + n2 = 0 Move the constant term to the right: Add '1085.714286' to each side of the equation. -1085.714286 + 6.142857143n + 1085.714286 + n2 = 0 + 1085.714286 Reorder the terms: -1085.714286 + 1085.714286 + 6.142857143n + n2 = 0 + 1085.714286 Combine like terms: -1085.714286 + 1085.714286 = 0.000000 0.000000 + 6.142857143n + n2 = 0 + 1085.714286 6.142857143n + n2 = 0 + 1085.714286 Combine like terms: 0 + 1085.714286 = 1085.714286 6.142857143n + n2 = 1085.714286 The n term is 6.142857143n. Take half its coefficient (3.071428572). Square it (9.433673473) and add it to both sides. Add '9.433673473' to each side of the equation. 6.142857143n + 9.433673473 + n2 = 1085.714286 + 9.433673473 Reorder the terms: 9.433673473 + 6.142857143n + n2 = 1085.714286 + 9.433673473 Combine like terms: 1085.714286 + 9.433673473 = 1095.147959473 9.433673473 + 6.142857143n + n2 = 1095.147959473 Factor a perfect square on the left side: (n + 3.071428572)(n + 3.071428572) = 1095.147959473 Calculate the square root of the right side: 33.0930198 Break this problem into two subproblems by setting (n + 3.071428572) equal to 33.0930198 and -33.0930198.Subproblem 1
n + 3.071428572 = 33.0930198 Simplifying n + 3.071428572 = 33.0930198 Reorder the terms: 3.071428572 + n = 33.0930198 Solving 3.071428572 + n = 33.0930198 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.071428572' to each side of the equation. 3.071428572 + -3.071428572 + n = 33.0930198 + -3.071428572 Combine like terms: 3.071428572 + -3.071428572 = 0.000000000 0.000000000 + n = 33.0930198 + -3.071428572 n = 33.0930198 + -3.071428572 Combine like terms: 33.0930198 + -3.071428572 = 30.021591228 n = 30.021591228 Simplifying n = 30.021591228Subproblem 2
n + 3.071428572 = -33.0930198 Simplifying n + 3.071428572 = -33.0930198 Reorder the terms: 3.071428572 + n = -33.0930198 Solving 3.071428572 + n = -33.0930198 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.071428572' to each side of the equation. 3.071428572 + -3.071428572 + n = -33.0930198 + -3.071428572 Combine like terms: 3.071428572 + -3.071428572 = 0.000000000 0.000000000 + n = -33.0930198 + -3.071428572 n = -33.0930198 + -3.071428572 Combine like terms: -33.0930198 + -3.071428572 = -36.164448372 n = -36.164448372 Simplifying n = -36.164448372Solution
The solution to the problem is based on the solutions from the subproblems. n = {30.021591228, -36.164448372}Solution
n = {30.021591228, -36.164448372}
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