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Simplifying 110n2 + 21n = 2 Reorder the terms: 21n + 110n2 = 2 Solving 21n + 110n2 = 2 Solving for variable 'n'. Reorder the terms: -2 + 21n + 110n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 21n + 110n2 = 0 Begin completing the square. Divide all terms by 110 the coefficient of the squared term: Divide each side by '110'. -0.01818181818 + 0.1909090909n + n2 = 0 Move the constant term to the right: Add '0.01818181818' to each side of the equation. -0.01818181818 + 0.1909090909n + 0.01818181818 + n2 = 0 + 0.01818181818 Reorder the terms: -0.01818181818 + 0.01818181818 + 0.1909090909n + n2 = 0 + 0.01818181818 Combine like terms: -0.01818181818 + 0.01818181818 = 0.00000000000 0.00000000000 + 0.1909090909n + n2 = 0 + 0.01818181818 0.1909090909n + n2 = 0 + 0.01818181818 Combine like terms: 0 + 0.01818181818 = 0.01818181818 0.1909090909n + n2 = 0.01818181818 The n term is 0.1909090909n. Take half its coefficient (0.09545454545). Square it (0.009111570247) and add it to both sides. Add '0.009111570247' to each side of the equation. 0.1909090909n + 0.009111570247 + n2 = 0.01818181818 + 0.009111570247 Reorder the terms: 0.009111570247 + 0.1909090909n + n2 = 0.01818181818 + 0.009111570247 Combine like terms: 0.01818181818 + 0.009111570247 = 0.027293388427 0.009111570247 + 0.1909090909n + n2 = 0.027293388427 Factor a perfect square on the left side: (n + 0.09545454545)(n + 0.09545454545) = 0.027293388427 Calculate the square root of the right side: 0.165207108 Break this problem into two subproblems by setting (n + 0.09545454545) equal to 0.165207108 and -0.165207108.Subproblem 1
n + 0.09545454545 = 0.165207108 Simplifying n + 0.09545454545 = 0.165207108 Reorder the terms: 0.09545454545 + n = 0.165207108 Solving 0.09545454545 + n = 0.165207108 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.09545454545' to each side of the equation. 0.09545454545 + -0.09545454545 + n = 0.165207108 + -0.09545454545 Combine like terms: 0.09545454545 + -0.09545454545 = 0.00000000000 0.00000000000 + n = 0.165207108 + -0.09545454545 n = 0.165207108 + -0.09545454545 Combine like terms: 0.165207108 + -0.09545454545 = 0.06975256255 n = 0.06975256255 Simplifying n = 0.06975256255Subproblem 2
n + 0.09545454545 = -0.165207108 Simplifying n + 0.09545454545 = -0.165207108 Reorder the terms: 0.09545454545 + n = -0.165207108 Solving 0.09545454545 + n = -0.165207108 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.09545454545' to each side of the equation. 0.09545454545 + -0.09545454545 + n = -0.165207108 + -0.09545454545 Combine like terms: 0.09545454545 + -0.09545454545 = 0.00000000000 0.00000000000 + n = -0.165207108 + -0.09545454545 n = -0.165207108 + -0.09545454545 Combine like terms: -0.165207108 + -0.09545454545 = -0.26066165345 n = -0.26066165345 Simplifying n = -0.26066165345Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.06975256255, -0.26066165345}
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