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Simplifying 5n2 + 18n = 9 Reorder the terms: 18n + 5n2 = 9 Solving 18n + 5n2 = 9 Solving for variable 'n'. Reorder the terms: -9 + 18n + 5n2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 18n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 3.6n + n2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 3.6n + 1.8 + n2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 3.6n + n2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 3.6n + n2 = 0 + 1.8 3.6n + n2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 3.6n + n2 = 1.8 The n term is 3.6n. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6n + 3.24 + n2 = 1.8 + 3.24 Reorder the terms: 3.24 + 3.6n + n2 = 1.8 + 3.24 Combine like terms: 1.8 + 3.24 = 5.04 3.24 + 3.6n + n2 = 5.04 Factor a perfect square on the left side: (n + 1.8)(n + 1.8) = 5.04 Calculate the square root of the right side: 2.244994432 Break this problem into two subproblems by setting (n + 1.8) equal to 2.244994432 and -2.244994432.Subproblem 1
n + 1.8 = 2.244994432 Simplifying n + 1.8 = 2.244994432 Reorder the terms: 1.8 + n = 2.244994432 Solving 1.8 + n = 2.244994432 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + n = 2.244994432 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + n = 2.244994432 + -1.8 n = 2.244994432 + -1.8 Combine like terms: 2.244994432 + -1.8 = 0.444994432 n = 0.444994432 Simplifying n = 0.444994432Subproblem 2
n + 1.8 = -2.244994432 Simplifying n + 1.8 = -2.244994432 Reorder the terms: 1.8 + n = -2.244994432 Solving 1.8 + n = -2.244994432 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + n = -2.244994432 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + n = -2.244994432 + -1.8 n = -2.244994432 + -1.8 Combine like terms: -2.244994432 + -1.8 = -4.044994432 n = -4.044994432 Simplifying n = -4.044994432Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.444994432, -4.044994432}
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