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Simplifying 5n2 + 5n = 6 Reorder the terms: 5n + 5n2 = 6 Solving 5n + 5n2 = 6 Solving for variable 'n'. Reorder the terms: -6 + 5n + 5n2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 5n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + n + n2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + n + 1.2 + n2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + n + n2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + n + n2 = 0 + 1.2 n + n2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 n + n2 = 1.2 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + n2 = 1.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + n2 = 1.2 + 0.25 Combine like terms: 1.2 + 0.25 = 1.45 1.25 + n2 = 1.45 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (n + 0.5) equal to 1.204159458 and -1.204159458.Subproblem 1
n + 0.5 = 1.204159458 Simplifying n + 0.5 = 1.204159458 Reorder the terms: 0.5 + n = 1.204159458 Solving 0.5 + n = 1.204159458 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 1.204159458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 1.204159458 + -0.5 n = 1.204159458 + -0.5 Combine like terms: 1.204159458 + -0.5 = 0.704159458 n = 0.704159458 Simplifying n = 0.704159458Subproblem 2
n + 0.5 = -1.204159458 Simplifying n + 0.5 = -1.204159458 Reorder the terms: 0.5 + n = -1.204159458 Solving 0.5 + n = -1.204159458 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -1.204159458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -1.204159458 + -0.5 n = -1.204159458 + -0.5 Combine like terms: -1.204159458 + -0.5 = -1.704159458 n = -1.704159458 Simplifying n = -1.704159458Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.704159458, -1.704159458}
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