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Simplifying 5n2 + -48n + 85 = 0 Reorder the terms: 85 + -48n + 5n2 = 0 Solving 85 + -48n + 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'. 17 + -9.6n + n2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -9.6n + -17 + n2 = 0 + -17 Reorder the terms: 17 + -17 + -9.6n + n2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -9.6n + n2 = 0 + -17 -9.6n + n2 = 0 + -17 Combine like terms: 0 + -17 = -17 -9.6n + n2 = -17 The n term is -9.6n. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6n + 23.04 + n2 = -17 + 23.04 Reorder the terms: 23.04 + -9.6n + n2 = -17 + 23.04 Combine like terms: -17 + 23.04 = 6.04 23.04 + -9.6n + n2 = 6.04 Factor a perfect square on the left side: (n + -4.8)(n + -4.8) = 6.04 Calculate the square root of the right side: 2.457641145 Break this problem into two subproblems by setting (n + -4.8) equal to 2.457641145 and -2.457641145.Subproblem 1
n + -4.8 = 2.457641145 Simplifying n + -4.8 = 2.457641145 Reorder the terms: -4.8 + n = 2.457641145 Solving -4.8 + n = 2.457641145 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + n = 2.457641145 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + n = 2.457641145 + 4.8 n = 2.457641145 + 4.8 Combine like terms: 2.457641145 + 4.8 = 7.257641145 n = 7.257641145 Simplifying n = 7.257641145Subproblem 2
n + -4.8 = -2.457641145 Simplifying n + -4.8 = -2.457641145 Reorder the terms: -4.8 + n = -2.457641145 Solving -4.8 + n = -2.457641145 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + n = -2.457641145 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + n = -2.457641145 + 4.8 n = -2.457641145 + 4.8 Combine like terms: -2.457641145 + 4.8 = 2.342358855 n = 2.342358855 Simplifying n = 2.342358855Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.257641145, 2.342358855}
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