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Simplifying 9n2 + -18n + -95 = 3 Reorder the terms: -95 + -18n + 9n2 = 3 Solving -95 + -18n + 9n2 = 3 Solving for variable 'n'. Reorder the terms: -95 + -3 + -18n + 9n2 = 3 + -3 Combine like terms: -95 + -3 = -98 -98 + -18n + 9n2 = 3 + -3 Combine like terms: 3 + -3 = 0 -98 + -18n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -10.88888889 + -2n + n2 = 0 Move the constant term to the right: Add '10.88888889' to each side of the equation. -10.88888889 + -2n + 10.88888889 + n2 = 0 + 10.88888889 Reorder the terms: -10.88888889 + 10.88888889 + -2n + n2 = 0 + 10.88888889 Combine like terms: -10.88888889 + 10.88888889 = 0.00000000 0.00000000 + -2n + n2 = 0 + 10.88888889 -2n + n2 = 0 + 10.88888889 Combine like terms: 0 + 10.88888889 = 10.88888889 -2n + n2 = 10.88888889 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 10.88888889 + 1 Reorder the terms: 1 + -2n + n2 = 10.88888889 + 1 Combine like terms: 10.88888889 + 1 = 11.88888889 1 + -2n + n2 = 11.88888889 Factor a perfect square on the left side: (n + -1)(n + -1) = 11.88888889 Calculate the square root of the right side: 3.448026811 Break this problem into two subproblems by setting (n + -1) equal to 3.448026811 and -3.448026811.Subproblem 1
n + -1 = 3.448026811 Simplifying n + -1 = 3.448026811 Reorder the terms: -1 + n = 3.448026811 Solving -1 + n = 3.448026811 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 3.448026811 + 1 Combine like terms: -1 + 1 = 0 0 + n = 3.448026811 + 1 n = 3.448026811 + 1 Combine like terms: 3.448026811 + 1 = 4.448026811 n = 4.448026811 Simplifying n = 4.448026811Subproblem 2
n + -1 = -3.448026811 Simplifying n + -1 = -3.448026811 Reorder the terms: -1 + n = -3.448026811 Solving -1 + n = -3.448026811 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -3.448026811 + 1 Combine like terms: -1 + 1 = 0 0 + n = -3.448026811 + 1 n = -3.448026811 + 1 Combine like terms: -3.448026811 + 1 = -2.448026811 n = -2.448026811 Simplifying n = -2.448026811Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.448026811, -2.448026811}
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