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Simplifying 10n2 + -10n + -4 = 0 Reorder the terms: -4 + -10n + 10n2 = 0 Solving -4 + -10n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -5n + 5n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -5n + 5n2)' equal to zero and attempt to solve: Simplifying -2 + -5n + 5n2 = 0 Solving -2 + -5n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -1n + n2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1n + 0.4 + n2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1n + n2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1n + n2 = 0 + 0.4 -1n + n2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1n + n2 = 0.4 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 0.4 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 0.4 + 0.25 Combine like terms: 0.4 + 0.25 = 0.65 0.25 + -1n + n2 = 0.65 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (n + -0.5) equal to 0.806225775 and -0.806225775.Subproblem 1
n + -0.5 = 0.806225775 Simplifying n + -0.5 = 0.806225775 Reorder the terms: -0.5 + n = 0.806225775 Solving -0.5 + n = 0.806225775 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 0.806225775 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 0.806225775 + 0.5 n = 0.806225775 + 0.5 Combine like terms: 0.806225775 + 0.5 = 1.306225775 n = 1.306225775 Simplifying n = 1.306225775Subproblem 2
n + -0.5 = -0.806225775 Simplifying n + -0.5 = -0.806225775 Reorder the terms: -0.5 + n = -0.806225775 Solving -0.5 + n = -0.806225775 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -0.806225775 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -0.806225775 + 0.5 n = -0.806225775 + 0.5 Combine like terms: -0.806225775 + 0.5 = -0.306225775 n = -0.306225775 Simplifying n = -0.306225775Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.306225775, -0.306225775}Solution
n = {1.306225775, -0.306225775}
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