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Simplifying -5n2 + -6n + 1 = 0 Reorder the terms: 1 + -6n + -5n2 = 0 Solving 1 + -6n + -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'. -0.2 + 1.2n + n2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 1.2n + 0.2 + n2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 1.2n + n2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 1.2n + n2 = 0 + 0.2 1.2n + n2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 1.2n + n2 = 0.2 The n term is 1.2n. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2n + 0.36 + n2 = 0.2 + 0.36 Reorder the terms: 0.36 + 1.2n + n2 = 0.2 + 0.36 Combine like terms: 0.2 + 0.36 = 0.56 0.36 + 1.2n + n2 = 0.56 Factor a perfect square on the left side: (n + 0.6)(n + 0.6) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (n + 0.6) equal to 0.748331477 and -0.748331477.Subproblem 1
n + 0.6 = 0.748331477 Simplifying n + 0.6 = 0.748331477 Reorder the terms: 0.6 + n = 0.748331477 Solving 0.6 + n = 0.748331477 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + n = 0.748331477 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = 0.748331477 + -0.6 n = 0.748331477 + -0.6 Combine like terms: 0.748331477 + -0.6 = 0.148331477 n = 0.148331477 Simplifying n = 0.148331477Subproblem 2
n + 0.6 = -0.748331477 Simplifying n + 0.6 = -0.748331477 Reorder the terms: 0.6 + n = -0.748331477 Solving 0.6 + n = -0.748331477 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + n = -0.748331477 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + n = -0.748331477 + -0.6 n = -0.748331477 + -0.6 Combine like terms: -0.748331477 + -0.6 = -1.348331477 n = -1.348331477 Simplifying n = -1.348331477Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.148331477, -1.348331477}
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