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Simplifying 2n2 + -9 = 18n Reorder the terms: -9 + 2n2 = 18n Solving -9 + 2n2 = 18n Solving for variable 'n'. Reorder the terms: -9 + -18n + 2n2 = 18n + -18n Combine like terms: 18n + -18n = 0 -9 + -18n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -9n + n2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -9n + 4.5 + n2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -9n + n2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -9n + n2 = 0 + 4.5 -9n + n2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -9n + n2 = 4.5 The n term is -9n. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9n + 20.25 + n2 = 4.5 + 20.25 Reorder the terms: 20.25 + -9n + n2 = 4.5 + 20.25 Combine like terms: 4.5 + 20.25 = 24.75 20.25 + -9n + n2 = 24.75 Factor a perfect square on the left side: (n + -4.5)(n + -4.5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (n + -4.5) equal to 4.974937186 and -4.974937186.Subproblem 1
n + -4.5 = 4.974937186 Simplifying n + -4.5 = 4.974937186 Reorder the terms: -4.5 + n = 4.974937186 Solving -4.5 + n = 4.974937186 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = 4.974937186 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 4.974937186 + 4.5 n = 4.974937186 + 4.5 Combine like terms: 4.974937186 + 4.5 = 9.474937186 n = 9.474937186 Simplifying n = 9.474937186Subproblem 2
n + -4.5 = -4.974937186 Simplifying n + -4.5 = -4.974937186 Reorder the terms: -4.5 + n = -4.974937186 Solving -4.5 + n = -4.974937186 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + n = -4.974937186 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -4.974937186 + 4.5 n = -4.974937186 + 4.5 Combine like terms: -4.974937186 + 4.5 = -0.474937186 n = -0.474937186 Simplifying n = -0.474937186Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.474937186, -0.474937186}
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