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Simplifying 5n2 + -120n + 24 = 0 Reorder the terms: 24 + -120n + 5n2 = 0 Solving 24 + -120n + 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 + -24n + n2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + -24n + -4.8 + n2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + -24n + n2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + -24n + n2 = 0 + -4.8 -24n + n2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 -24n + n2 = -4.8 The n term is -24n. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24n + 144 + n2 = -4.8 + 144 Reorder the terms: 144 + -24n + n2 = -4.8 + 144 Combine like terms: -4.8 + 144 = 139.2 144 + -24n + n2 = 139.2 Factor a perfect square on the left side: (n + -12)(n + -12) = 139.2 Calculate the square root of the right side: 11.798304963 Break this problem into two subproblems by setting (n + -12) equal to 11.798304963 and -11.798304963.Subproblem 1
n + -12 = 11.798304963 Simplifying n + -12 = 11.798304963 Reorder the terms: -12 + n = 11.798304963 Solving -12 + n = 11.798304963 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + n = 11.798304963 + 12 Combine like terms: -12 + 12 = 0 0 + n = 11.798304963 + 12 n = 11.798304963 + 12 Combine like terms: 11.798304963 + 12 = 23.798304963 n = 23.798304963 Simplifying n = 23.798304963Subproblem 2
n + -12 = -11.798304963 Simplifying n + -12 = -11.798304963 Reorder the terms: -12 + n = -11.798304963 Solving -12 + n = -11.798304963 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + n = -11.798304963 + 12 Combine like terms: -12 + 12 = 0 0 + n = -11.798304963 + 12 n = -11.798304963 + 12 Combine like terms: -11.798304963 + 12 = 0.201695037 n = 0.201695037 Simplifying n = 0.201695037Solution
The solution to the problem is based on the solutions from the subproblems. n = {23.798304963, 0.201695037}
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