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Simplifying 5n2 = 4n + 6 Reorder the terms: 5n2 = 6 + 4n Solving 5n2 = 6 + 4n Solving for variable 'n'. Reorder the terms: -6 + -4n + 5n2 = 6 + 4n + -6 + -4n Reorder the terms: -6 + -4n + 5n2 = 6 + -6 + 4n + -4n Combine like terms: 6 + -6 = 0 -6 + -4n + 5n2 = 0 + 4n + -4n -6 + -4n + 5n2 = 4n + -4n Combine like terms: 4n + -4n = 0 -6 + -4n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -0.8n + n2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.8n + 1.2 + n2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.8n + n2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.8n + n2 = 0 + 1.2 -0.8n + n2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.8n + n2 = 1.2 The n term is -0.8n. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8n + 0.16 + n2 = 1.2 + 0.16 Reorder the terms: 0.16 + -0.8n + n2 = 1.2 + 0.16 Combine like terms: 1.2 + 0.16 = 1.36 0.16 + -0.8n + n2 = 1.36 Factor a perfect square on the left side: (n + -0.4)(n + -0.4) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (n + -0.4) equal to 1.166190379 and -1.166190379.Subproblem 1
n + -0.4 = 1.166190379 Simplifying n + -0.4 = 1.166190379 Reorder the terms: -0.4 + n = 1.166190379 Solving -0.4 + n = 1.166190379 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + n = 1.166190379 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + n = 1.166190379 + 0.4 n = 1.166190379 + 0.4 Combine like terms: 1.166190379 + 0.4 = 1.566190379 n = 1.566190379 Simplifying n = 1.566190379Subproblem 2
n + -0.4 = -1.166190379 Simplifying n + -0.4 = -1.166190379 Reorder the terms: -0.4 + n = -1.166190379 Solving -0.4 + n = -1.166190379 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + n = -1.166190379 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + n = -1.166190379 + 0.4 n = -1.166190379 + 0.4 Combine like terms: -1.166190379 + 0.4 = -0.766190379 n = -0.766190379 Simplifying n = -0.766190379Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.566190379, -0.766190379}
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