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Simplifying 5n2 + 4n + -8 = 0 Reorder the terms: -8 + 4n + 5n2 = 0 Solving -8 + 4n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 0.8n + n2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 0.8n + 1.6 + n2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 0.8n + n2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 0.8n + n2 = 0 + 1.6 0.8n + n2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 0.8n + n2 = 1.6 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 = 1.6 + 0.16 Reorder the terms: 0.16 + 0.8n + n2 = 1.6 + 0.16 Combine like terms: 1.6 + 0.16 = 1.76 0.16 + 0.8n + n2 = 1.76 Factor a perfect square on the left side: (n + 0.4)(n + 0.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (n + 0.4) equal to 1.326649916 and -1.326649916.Subproblem 1
n + 0.4 = 1.326649916 Simplifying n + 0.4 = 1.326649916 Reorder the terms: 0.4 + n = 1.326649916 Solving 0.4 + n = 1.326649916 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 = 1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + n = 1.326649916 + -0.4 n = 1.326649916 + -0.4 Combine like terms: 1.326649916 + -0.4 = 0.926649916 n = 0.926649916 Simplifying n = 0.926649916Subproblem 2
n + 0.4 = -1.326649916 Simplifying n + 0.4 = -1.326649916 Reorder the terms: 0.4 + n = -1.326649916 Solving 0.4 + n = -1.326649916 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 = -1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + n = -1.326649916 + -0.4 n = -1.326649916 + -0.4 Combine like terms: -1.326649916 + -0.4 = -1.726649916 n = -1.726649916 Simplifying n = -1.726649916Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.926649916, -1.726649916}
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