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Simplifying 1436400 = c(500c + 7182) Reorder the terms: 1436400 = c(7182 + 500c) 1436400 = (7182 * c + 500c * c) 1436400 = (7182c + 500c2) Solving 1436400 = 7182c + 500c2 Solving for variable 'c'. Reorder the terms: 1436400 + -7182c + -500c2 = 7182c + -7182c + 500c2 + -500c2 Combine like terms: 7182c + -7182c = 0 1436400 + -7182c + -500c2 = 0 + 500c2 + -500c2 1436400 + -7182c + -500c2 = 500c2 + -500c2 Combine like terms: 500c2 + -500c2 = 0 1436400 + -7182c + -500c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(718200 + -3591c + -250c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(718200 + -3591c + -250c2)' equal to zero and attempt to solve: Simplifying 718200 + -3591c + -250c2 = 0 Solving 718200 + -3591c + -250c2 = 0 Begin completing the square. Divide all terms by -250 the coefficient of the squared term: Divide each side by '-250'. -2872.8 + 14.364c + c2 = 0.0 Move the constant term to the right: Add '2872.8' to each side of the equation. -2872.8 + 14.364c + 2872.8 + c2 = 0.0 + 2872.8 Reorder the terms: -2872.8 + 2872.8 + 14.364c + c2 = 0.0 + 2872.8 Combine like terms: -2872.8 + 2872.8 = 0.0 0.0 + 14.364c + c2 = 0.0 + 2872.8 14.364c + c2 = 0.0 + 2872.8 Combine like terms: 0.0 + 2872.8 = 2872.8 14.364c + c2 = 2872.8 The c term is 14.364c. Take half its coefficient (7.182). Square it (51.581124) and add it to both sides. Add '51.581124' to each side of the equation. 14.364c + 51.581124 + c2 = 2872.8 + 51.581124 Reorder the terms: 51.581124 + 14.364c + c2 = 2872.8 + 51.581124 Combine like terms: 2872.8 + 51.581124 = 2924.381124 51.581124 + 14.364c + c2 = 2924.381124 Factor a perfect square on the left side: (c + 7.182)(c + 7.182) = 2924.381124 Calculate the square root of the right side: 54.077547319 Break this problem into two subproblems by setting (c + 7.182) equal to 54.077547319 and -54.077547319.Subproblem 1
c + 7.182 = 54.077547319 Simplifying c + 7.182 = 54.077547319 Reorder the terms: 7.182 + c = 54.077547319 Solving 7.182 + c = 54.077547319 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7.182' to each side of the equation. 7.182 + -7.182 + c = 54.077547319 + -7.182 Combine like terms: 7.182 + -7.182 = 0.000 0.000 + c = 54.077547319 + -7.182 c = 54.077547319 + -7.182 Combine like terms: 54.077547319 + -7.182 = 46.895547319 c = 46.895547319 Simplifying c = 46.895547319Subproblem 2
c + 7.182 = -54.077547319 Simplifying c + 7.182 = -54.077547319 Reorder the terms: 7.182 + c = -54.077547319 Solving 7.182 + c = -54.077547319 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7.182' to each side of the equation. 7.182 + -7.182 + c = -54.077547319 + -7.182 Combine like terms: 7.182 + -7.182 = 0.000 0.000 + c = -54.077547319 + -7.182 c = -54.077547319 + -7.182 Combine like terms: -54.077547319 + -7.182 = -61.259547319 c = -61.259547319 Simplifying c = -61.259547319Solution
The solution to the problem is based on the solutions from the subproblems. c = {46.895547319, -61.259547319}Solution
c = {46.895547319, -61.259547319}
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