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Simplifying 5n2 = -8n + 7 Reorder the terms: 5n2 = 7 + -8n Solving 5n2 = 7 + -8n Solving for variable 'n'. Reorder the terms: -7 + 8n + 5n2 = 7 + -8n + -7 + 8n Reorder the terms: -7 + 8n + 5n2 = 7 + -7 + -8n + 8n Combine like terms: 7 + -7 = 0 -7 + 8n + 5n2 = 0 + -8n + 8n -7 + 8n + 5n2 = -8n + 8n Combine like terms: -8n + 8n = 0 -7 + 8n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 1.6n + n2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 1.6n + 1.4 + n2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 1.6n + n2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 1.6n + n2 = 0 + 1.4 1.6n + n2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 1.6n + n2 = 1.4 The n term is 1.6n. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6n + 0.64 + n2 = 1.4 + 0.64 Reorder the terms: 0.64 + 1.6n + n2 = 1.4 + 0.64 Combine like terms: 1.4 + 0.64 = 2.04 0.64 + 1.6n + n2 = 2.04 Factor a perfect square on the left side: (n + 0.8)(n + 0.8) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (n + 0.8) equal to 1.428285686 and -1.428285686.Subproblem 1
n + 0.8 = 1.428285686 Simplifying n + 0.8 = 1.428285686 Reorder the terms: 0.8 + n = 1.428285686 Solving 0.8 + n = 1.428285686 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + n = 1.428285686 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + n = 1.428285686 + -0.8 n = 1.428285686 + -0.8 Combine like terms: 1.428285686 + -0.8 = 0.628285686 n = 0.628285686 Simplifying n = 0.628285686Subproblem 2
n + 0.8 = -1.428285686 Simplifying n + 0.8 = -1.428285686 Reorder the terms: 0.8 + n = -1.428285686 Solving 0.8 + n = -1.428285686 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + n = -1.428285686 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + n = -1.428285686 + -0.8 n = -1.428285686 + -0.8 Combine like terms: -1.428285686 + -0.8 = -2.228285686 n = -2.228285686 Simplifying n = -2.228285686Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.628285686, -2.228285686}
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