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Simplifying 10n2 + -16 = 8n Reorder the terms: -16 + 10n2 = 8n Solving -16 + 10n2 = 8n Solving for variable 'n'. Reorder the terms: -16 + -8n + 10n2 = 8n + -8n Combine like terms: 8n + -8n = 0 -16 + -8n + 10n2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -4n + 5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -4n + 5n2)' equal to zero and attempt to solve: Simplifying -8 + -4n + 5n2 = 0 Solving -8 + -4n + 5n2 = 0 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 = 1.726649916 n = 1.726649916 Simplifying n = 1.726649916Subproblem 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 = -0.926649916 n = -0.926649916 Simplifying n = -0.926649916Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.726649916, -0.926649916}Solution
n = {1.726649916, -0.926649916}
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