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Simplifying 5n2 + -3 = 4n Reorder the terms: -3 + 5n2 = 4n Solving -3 + 5n2 = 4n Solving for variable 'n'. Reorder the terms: -3 + -4n + 5n2 = 4n + -4n Combine like terms: 4n + -4n = 0 -3 + -4n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -0.8n + n2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.8n + 0.6 + n2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.8n + n2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.8n + n2 = 0 + 0.6 -0.8n + n2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.8n + n2 = 0.6 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 = 0.6 + 0.16 Reorder the terms: 0.16 + -0.8n + n2 = 0.6 + 0.16 Combine like terms: 0.6 + 0.16 = 0.76 0.16 + -0.8n + n2 = 0.76 Factor a perfect square on the left side: (n + -0.4)(n + -0.4) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (n + -0.4) equal to 0.871779789 and -0.871779789.Subproblem 1
n + -0.4 = 0.871779789 Simplifying n + -0.4 = 0.871779789 Reorder the terms: -0.4 + n = 0.871779789 Solving -0.4 + n = 0.871779789 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 = 0.871779789 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + n = 0.871779789 + 0.4 n = 0.871779789 + 0.4 Combine like terms: 0.871779789 + 0.4 = 1.271779789 n = 1.271779789 Simplifying n = 1.271779789Subproblem 2
n + -0.4 = -0.871779789 Simplifying n + -0.4 = -0.871779789 Reorder the terms: -0.4 + n = -0.871779789 Solving -0.4 + n = -0.871779789 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 = -0.871779789 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + n = -0.871779789 + 0.4 n = -0.871779789 + 0.4 Combine like terms: -0.871779789 + 0.4 = -0.471779789 n = -0.471779789 Simplifying n = -0.471779789Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.271779789, -0.471779789}
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