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Simplifying 10n2 + 490n + -4000 = 0 Reorder the terms: -4000 + 490n + 10n2 = 0 Solving -4000 + 490n + 10n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '10'. 10(-400 + 49n + n2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-400 + 49n + n2)' equal to zero and attempt to solve: Simplifying -400 + 49n + n2 = 0 Solving -400 + 49n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 49n + 400 + n2 = 0 + 400 Reorder the terms: -400 + 400 + 49n + n2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 49n + n2 = 0 + 400 49n + n2 = 0 + 400 Combine like terms: 0 + 400 = 400 49n + n2 = 400 The n term is 49n. Take half its coefficient (24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. 49n + 600.25 + n2 = 400 + 600.25 Reorder the terms: 600.25 + 49n + n2 = 400 + 600.25 Combine like terms: 400 + 600.25 = 1000.25 600.25 + 49n + n2 = 1000.25 Factor a perfect square on the left side: (n + 24.5)(n + 24.5) = 1000.25 Calculate the square root of the right side: 31.626729202 Break this problem into two subproblems by setting (n + 24.5) equal to 31.626729202 and -31.626729202.Subproblem 1
n + 24.5 = 31.626729202 Simplifying n + 24.5 = 31.626729202 Reorder the terms: 24.5 + n = 31.626729202 Solving 24.5 + n = 31.626729202 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + n = 31.626729202 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + n = 31.626729202 + -24.5 n = 31.626729202 + -24.5 Combine like terms: 31.626729202 + -24.5 = 7.126729202 n = 7.126729202 Simplifying n = 7.126729202Subproblem 2
n + 24.5 = -31.626729202 Simplifying n + 24.5 = -31.626729202 Reorder the terms: 24.5 + n = -31.626729202 Solving 24.5 + n = -31.626729202 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + n = -31.626729202 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + n = -31.626729202 + -24.5 n = -31.626729202 + -24.5 Combine like terms: -31.626729202 + -24.5 = -56.126729202 n = -56.126729202 Simplifying n = -56.126729202Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.126729202, -56.126729202}Solution
n = {7.126729202, -56.126729202}
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