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Simplifying 5n2 + 18n + 12 = 0 Reorder the terms: 12 + 18n + 5n2 = 0 Solving 12 + 18n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 3.6n + n2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 3.6n + -2.4 + n2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 3.6n + n2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 3.6n + n2 = 0 + -2.4 3.6n + n2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 3.6n + n2 = -2.4 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 = -2.4 + 3.24 Reorder the terms: 3.24 + 3.6n + n2 = -2.4 + 3.24 Combine like terms: -2.4 + 3.24 = 0.84 3.24 + 3.6n + n2 = 0.84 Factor a perfect square on the left side: (n + 1.8)(n + 1.8) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (n + 1.8) equal to 0.916515139 and -0.916515139.Subproblem 1
n + 1.8 = 0.916515139 Simplifying n + 1.8 = 0.916515139 Reorder the terms: 1.8 + n = 0.916515139 Solving 1.8 + n = 0.916515139 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 = 0.916515139 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + n = 0.916515139 + -1.8 n = 0.916515139 + -1.8 Combine like terms: 0.916515139 + -1.8 = -0.883484861 n = -0.883484861 Simplifying n = -0.883484861Subproblem 2
n + 1.8 = -0.916515139 Simplifying n + 1.8 = -0.916515139 Reorder the terms: 1.8 + n = -0.916515139 Solving 1.8 + n = -0.916515139 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 = -0.916515139 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + n = -0.916515139 + -1.8 n = -0.916515139 + -1.8 Combine like terms: -0.916515139 + -1.8 = -2.716515139 n = -2.716515139 Simplifying n = -2.716515139Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.883484861, -2.716515139}
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