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Simplifying 5c3 + 55c2 + 10c = 0 Reorder the terms: 10c + 55c2 + 5c3 = 0 Solving 10c + 55c2 + 5c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '5c'. 5c(2 + 11c + c2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(2 + 11c + c2)' equal to zero and attempt to solve: Simplifying 2 + 11c + c2 = 0 Solving 2 + 11c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 11c + -2 + c2 = 0 + -2 Reorder the terms: 2 + -2 + 11c + c2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 11c + c2 = 0 + -2 11c + c2 = 0 + -2 Combine like terms: 0 + -2 = -2 11c + c2 = -2 The c term is 11c. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11c + 30.25 + c2 = -2 + 30.25 Reorder the terms: 30.25 + 11c + c2 = -2 + 30.25 Combine like terms: -2 + 30.25 = 28.25 30.25 + 11c + c2 = 28.25 Factor a perfect square on the left side: (c + 5.5)(c + 5.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (c + 5.5) equal to 5.315072906 and -5.315072906.Subproblem 1
c + 5.5 = 5.315072906 Simplifying c + 5.5 = 5.315072906 Reorder the terms: 5.5 + c = 5.315072906 Solving 5.5 + c = 5.315072906 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + c = 5.315072906 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + c = 5.315072906 + -5.5 c = 5.315072906 + -5.5 Combine like terms: 5.315072906 + -5.5 = -0.184927094 c = -0.184927094 Simplifying c = -0.184927094Subproblem 2
c + 5.5 = -5.315072906 Simplifying c + 5.5 = -5.315072906 Reorder the terms: 5.5 + c = -5.315072906 Solving 5.5 + c = -5.315072906 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + c = -5.315072906 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + c = -5.315072906 + -5.5 c = -5.315072906 + -5.5 Combine like terms: -5.315072906 + -5.5 = -10.815072906 c = -10.815072906 Simplifying c = -10.815072906Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.184927094, -10.815072906}Solution
c = {0, -0.184927094, -10.815072906}
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