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Simplifying 5c3 + 3c2 + -35c = 0 Reorder the terms: -35c + 3c2 + 5c3 = 0 Solving -35c + 3c2 + 5c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c'. c(-35 + 3c + 5c2) = 0Subproblem 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 '(-35 + 3c + 5c2)' equal to zero and attempt to solve: Simplifying -35 + 3c + 5c2 = 0 Solving -35 + 3c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + 0.6c + c2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 0.6c + 7 + c2 = 0 + 7 Reorder the terms: -7 + 7 + 0.6c + c2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 0.6c + c2 = 0 + 7 0.6c + c2 = 0 + 7 Combine like terms: 0 + 7 = 7 0.6c + c2 = 7 The c term is 0.6c. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6c + 0.09 + c2 = 7 + 0.09 Reorder the terms: 0.09 + 0.6c + c2 = 7 + 0.09 Combine like terms: 7 + 0.09 = 7.09 0.09 + 0.6c + c2 = 7.09 Factor a perfect square on the left side: (c + 0.3)(c + 0.3) = 7.09 Calculate the square root of the right side: 2.662705391 Break this problem into two subproblems by setting (c + 0.3) equal to 2.662705391 and -2.662705391.Subproblem 1
c + 0.3 = 2.662705391 Simplifying c + 0.3 = 2.662705391 Reorder the terms: 0.3 + c = 2.662705391 Solving 0.3 + c = 2.662705391 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + c = 2.662705391 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + c = 2.662705391 + -0.3 c = 2.662705391 + -0.3 Combine like terms: 2.662705391 + -0.3 = 2.362705391 c = 2.362705391 Simplifying c = 2.362705391Subproblem 2
c + 0.3 = -2.662705391 Simplifying c + 0.3 = -2.662705391 Reorder the terms: 0.3 + c = -2.662705391 Solving 0.3 + c = -2.662705391 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + c = -2.662705391 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + c = -2.662705391 + -0.3 c = -2.662705391 + -0.3 Combine like terms: -2.662705391 + -0.3 = -2.962705391 c = -2.962705391 Simplifying c = -2.962705391Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.362705391, -2.962705391}Solution
c = {0, 2.362705391, -2.962705391}
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