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Simplifying 5n2 + 4n = 4 Reorder the terms: 4n + 5n2 = 4 Solving 4n + 5n2 = 4 Solving for variable 'n'. Reorder the terms: -4 + 4n + 5n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 4n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 0.8n + n2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.8n + 0.8 + n2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.8n + n2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.8n + n2 = 0 + 0.8 0.8n + n2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.8n + n2 = 0.8 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 = 0.8 + 0.16 Reorder the terms: 0.16 + 0.8n + n2 = 0.8 + 0.16 Combine like terms: 0.8 + 0.16 = 0.96 0.16 + 0.8n + n2 = 0.96 Factor a perfect square on the left side: (n + 0.4)(n + 0.4) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (n + 0.4) equal to 0.979795897 and -0.979795897.Subproblem 1
n + 0.4 = 0.979795897 Simplifying n + 0.4 = 0.979795897 Reorder the terms: 0.4 + n = 0.979795897 Solving 0.4 + n = 0.979795897 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 = 0.979795897 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + n = 0.979795897 + -0.4 n = 0.979795897 + -0.4 Combine like terms: 0.979795897 + -0.4 = 0.579795897 n = 0.579795897 Simplifying n = 0.579795897Subproblem 2
n + 0.4 = -0.979795897 Simplifying n + 0.4 = -0.979795897 Reorder the terms: 0.4 + n = -0.979795897 Solving 0.4 + n = -0.979795897 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 = -0.979795897 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + n = -0.979795897 + -0.4 n = -0.979795897 + -0.4 Combine like terms: -0.979795897 + -0.4 = -1.379795897 n = -1.379795897 Simplifying n = -1.379795897Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.579795897, -1.379795897}
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