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Simplifying 20 = -0.2n(n) + 7.2n + 1.5 Multiply n * n 20 = -0.2n2 + 7.2n + 1.5 Reorder the terms: 20 = 1.5 + 7.2n + -0.2n2 Solving 20 = 1.5 + 7.2n + -0.2n2 Solving for variable 'n'. Combine like terms: 20 + -1.5 = 18.5 18.5 + -7.2n + 0.2n2 = 1.5 + 7.2n + -0.2n2 + -1.5 + -7.2n + 0.2n2 Reorder the terms: 18.5 + -7.2n + 0.2n2 = 1.5 + -1.5 + 7.2n + -7.2n + -0.2n2 + 0.2n2 Combine like terms: 1.5 + -1.5 = 0.0 18.5 + -7.2n + 0.2n2 = 0.0 + 7.2n + -7.2n + -0.2n2 + 0.2n2 18.5 + -7.2n + 0.2n2 = 7.2n + -7.2n + -0.2n2 + 0.2n2 Combine like terms: 7.2n + -7.2n = 0.0 18.5 + -7.2n + 0.2n2 = 0.0 + -0.2n2 + 0.2n2 18.5 + -7.2n + 0.2n2 = -0.2n2 + 0.2n2 Combine like terms: -0.2n2 + 0.2n2 = 0.0 18.5 + -7.2n + 0.2n2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 92.5 + -36n + n2 = 0 Move the constant term to the right: Add '-92.5' to each side of the equation. 92.5 + -36n + -92.5 + n2 = 0 + -92.5 Reorder the terms: 92.5 + -92.5 + -36n + n2 = 0 + -92.5 Combine like terms: 92.5 + -92.5 = 0.0 0.0 + -36n + n2 = 0 + -92.5 -36n + n2 = 0 + -92.5 Combine like terms: 0 + -92.5 = -92.5 -36n + n2 = -92.5 The n term is -36n. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36n + 324 + n2 = -92.5 + 324 Reorder the terms: 324 + -36n + n2 = -92.5 + 324 Combine like terms: -92.5 + 324 = 231.5 324 + -36n + n2 = 231.5 Factor a perfect square on the left side: (n + -18)(n + -18) = 231.5 Calculate the square root of the right side: 15.215124055 Break this problem into two subproblems by setting (n + -18) equal to 15.215124055 and -15.215124055.Subproblem 1
n + -18 = 15.215124055 Simplifying n + -18 = 15.215124055 Reorder the terms: -18 + n = 15.215124055 Solving -18 + n = 15.215124055 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + n = 15.215124055 + 18 Combine like terms: -18 + 18 = 0 0 + n = 15.215124055 + 18 n = 15.215124055 + 18 Combine like terms: 15.215124055 + 18 = 33.215124055 n = 33.215124055 Simplifying n = 33.215124055Subproblem 2
n + -18 = -15.215124055 Simplifying n + -18 = -15.215124055 Reorder the terms: -18 + n = -15.215124055 Solving -18 + n = -15.215124055 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + n = -15.215124055 + 18 Combine like terms: -18 + 18 = 0 0 + n = -15.215124055 + 18 n = -15.215124055 + 18 Combine like terms: -15.215124055 + 18 = 2.784875945 n = 2.784875945 Simplifying n = 2.784875945Solution
The solution to the problem is based on the solutions from the subproblems. n = {33.215124055, 2.784875945}
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