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Simplifying n2 = 20n + -10 Reorder the terms: n2 = -10 + 20n Solving n2 = -10 + 20n Solving for variable 'n'. Reorder the terms: 10 + -20n + n2 = -10 + 20n + 10 + -20n Reorder the terms: 10 + -20n + n2 = -10 + 10 + 20n + -20n Combine like terms: -10 + 10 = 0 10 + -20n + n2 = 0 + 20n + -20n 10 + -20n + n2 = 20n + -20n Combine like terms: 20n + -20n = 0 10 + -20n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -20n + -10 + n2 = 0 + -10 Reorder the terms: 10 + -10 + -20n + n2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -20n + n2 = 0 + -10 -20n + n2 = 0 + -10 Combine like terms: 0 + -10 = -10 -20n + n2 = -10 The n term is -20n. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20n + 100 + n2 = -10 + 100 Reorder the terms: 100 + -20n + n2 = -10 + 100 Combine like terms: -10 + 100 = 90 100 + -20n + n2 = 90 Factor a perfect square on the left side: (n + -10)(n + -10) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (n + -10) equal to 9.486832981 and -9.486832981.Subproblem 1
n + -10 = 9.486832981 Simplifying n + -10 = 9.486832981 Reorder the terms: -10 + n = 9.486832981 Solving -10 + n = 9.486832981 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + n = 9.486832981 + 10 Combine like terms: -10 + 10 = 0 0 + n = 9.486832981 + 10 n = 9.486832981 + 10 Combine like terms: 9.486832981 + 10 = 19.486832981 n = 19.486832981 Simplifying n = 19.486832981Subproblem 2
n + -10 = -9.486832981 Simplifying n + -10 = -9.486832981 Reorder the terms: -10 + n = -9.486832981 Solving -10 + n = -9.486832981 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + n = -9.486832981 + 10 Combine like terms: -10 + 10 = 0 0 + n = -9.486832981 + 10 n = -9.486832981 + 10 Combine like terms: -9.486832981 + 10 = 0.513167019 n = 0.513167019 Simplifying n = 0.513167019Solution
The solution to the problem is based on the solutions from the subproblems. n = {19.486832981, 0.513167019}
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