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Simplifying 18n2 + -25n + -81 = 0 Reorder the terms: -81 + -25n + 18n2 = 0 Solving -81 + -25n + 18n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -4.5 + -1.388888889n + n2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -1.388888889n + 4.5 + n2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -1.388888889n + n2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -1.388888889n + n2 = 0 + 4.5 -1.388888889n + n2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -1.388888889n + n2 = 4.5 The n term is -1.388888889n. Take half its coefficient (-0.6944444445). Square it (0.4822530865) and add it to both sides. Add '0.4822530865' to each side of the equation. -1.388888889n + 0.4822530865 + n2 = 4.5 + 0.4822530865 Reorder the terms: 0.4822530865 + -1.388888889n + n2 = 4.5 + 0.4822530865 Combine like terms: 4.5 + 0.4822530865 = 4.9822530865 0.4822530865 + -1.388888889n + n2 = 4.9822530865 Factor a perfect square on the left side: (n + -0.6944444445)(n + -0.6944444445) = 4.9822530865 Calculate the square root of the right side: 2.232096119 Break this problem into two subproblems by setting (n + -0.6944444445) equal to 2.232096119 and -2.232096119.Subproblem 1
n + -0.6944444445 = 2.232096119 Simplifying n + -0.6944444445 = 2.232096119 Reorder the terms: -0.6944444445 + n = 2.232096119 Solving -0.6944444445 + n = 2.232096119 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6944444445' to each side of the equation. -0.6944444445 + 0.6944444445 + n = 2.232096119 + 0.6944444445 Combine like terms: -0.6944444445 + 0.6944444445 = 0.0000000000 0.0000000000 + n = 2.232096119 + 0.6944444445 n = 2.232096119 + 0.6944444445 Combine like terms: 2.232096119 + 0.6944444445 = 2.9265405635 n = 2.9265405635 Simplifying n = 2.9265405635Subproblem 2
n + -0.6944444445 = -2.232096119 Simplifying n + -0.6944444445 = -2.232096119 Reorder the terms: -0.6944444445 + n = -2.232096119 Solving -0.6944444445 + n = -2.232096119 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6944444445' to each side of the equation. -0.6944444445 + 0.6944444445 + n = -2.232096119 + 0.6944444445 Combine like terms: -0.6944444445 + 0.6944444445 = 0.0000000000 0.0000000000 + n = -2.232096119 + 0.6944444445 n = -2.232096119 + 0.6944444445 Combine like terms: -2.232096119 + 0.6944444445 = -1.5376516745 n = -1.5376516745 Simplifying n = -1.5376516745Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.9265405635, -1.5376516745}
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