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Simplifying 5n2 = 8n + 10 Reorder the terms: 5n2 = 10 + 8n Solving 5n2 = 10 + 8n Solving for variable 'n'. Reorder the terms: -10 + -8n + 5n2 = 10 + 8n + -10 + -8n Reorder the terms: -10 + -8n + 5n2 = 10 + -10 + 8n + -8n Combine like terms: 10 + -10 = 0 -10 + -8n + 5n2 = 0 + 8n + -8n -10 + -8n + 5n2 = 8n + -8n Combine like terms: 8n + -8n = 0 -10 + -8n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -1.6n + n2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.6n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + -1.6n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.6n + n2 = 0 + 2 -1.6n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.6n + n2 = 2 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 = 2 + 0.64 Reorder the terms: 0.64 + -1.6n + n2 = 2 + 0.64 Combine like terms: 2 + 0.64 = 2.64 0.64 + -1.6n + n2 = 2.64 Factor a perfect square on the left side: (n + -0.8)(n + -0.8) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (n + -0.8) equal to 1.624807681 and -1.624807681.Subproblem 1
n + -0.8 = 1.624807681 Simplifying n + -0.8 = 1.624807681 Reorder the terms: -0.8 + n = 1.624807681 Solving -0.8 + n = 1.624807681 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 = 1.624807681 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + n = 1.624807681 + 0.8 n = 1.624807681 + 0.8 Combine like terms: 1.624807681 + 0.8 = 2.424807681 n = 2.424807681 Simplifying n = 2.424807681Subproblem 2
n + -0.8 = -1.624807681 Simplifying n + -0.8 = -1.624807681 Reorder the terms: -0.8 + n = -1.624807681 Solving -0.8 + n = -1.624807681 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 = -1.624807681 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + n = -1.624807681 + 0.8 n = -1.624807681 + 0.8 Combine like terms: -1.624807681 + 0.8 = -0.824807681 n = -0.824807681 Simplifying n = -0.824807681Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.424807681, -0.824807681}
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