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Simplifying 9n2 + -9n + -18 = 2 Reorder the terms: -18 + -9n + 9n2 = 2 Solving -18 + -9n + 9n2 = 2 Solving for variable 'n'. Reorder the terms: -18 + -2 + -9n + 9n2 = 2 + -2 Combine like terms: -18 + -2 = -20 -20 + -9n + 9n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -20 + -9n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -1n + n2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -1n + 2.222222222 + n2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -1n + n2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -1n + n2 = 0 + 2.222222222 -1n + n2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -1n + n2 = 2.222222222 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 2.222222222 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 2.222222222 + 0.25 Combine like terms: 2.222222222 + 0.25 = 2.472222222 0.25 + -1n + n2 = 2.472222222 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 2.472222222 Calculate the square root of the right side: 1.572330189 Break this problem into two subproblems by setting (n + -0.5) equal to 1.572330189 and -1.572330189.Subproblem 1
n + -0.5 = 1.572330189 Simplifying n + -0.5 = 1.572330189 Reorder the terms: -0.5 + n = 1.572330189 Solving -0.5 + n = 1.572330189 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 1.572330189 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 1.572330189 + 0.5 n = 1.572330189 + 0.5 Combine like terms: 1.572330189 + 0.5 = 2.072330189 n = 2.072330189 Simplifying n = 2.072330189Subproblem 2
n + -0.5 = -1.572330189 Simplifying n + -0.5 = -1.572330189 Reorder the terms: -0.5 + n = -1.572330189 Solving -0.5 + n = -1.572330189 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -1.572330189 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -1.572330189 + 0.5 n = -1.572330189 + 0.5 Combine like terms: -1.572330189 + 0.5 = -1.072330189 n = -1.072330189 Simplifying n = -1.072330189Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.072330189, -1.072330189}
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