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Simplifying 3c3 + 24c2 + 27c = 0 Reorder the terms: 27c + 24c2 + 3c3 = 0 Solving 27c + 24c2 + 3c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3c'. 3c(9 + 8c + c2) = 0 Ignore the factor 3.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 '(9 + 8c + c2)' equal to zero and attempt to solve: Simplifying 9 + 8c + c2 = 0 Solving 9 + 8c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8c + -9 + c2 = 0 + -9 Reorder the terms: 9 + -9 + 8c + c2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8c + c2 = 0 + -9 8c + c2 = 0 + -9 Combine like terms: 0 + -9 = -9 8c + c2 = -9 The c term is 8c. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8c + 16 + c2 = -9 + 16 Reorder the terms: 16 + 8c + c2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8c + c2 = 7 Factor a perfect square on the left side: (c + 4)(c + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (c + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
c + 4 = 2.645751311 Simplifying c + 4 = 2.645751311 Reorder the terms: 4 + c = 2.645751311 Solving 4 + c = 2.645751311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + c = 2.645751311 + -4 c = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 c = -1.354248689 Simplifying c = -1.354248689Subproblem 2
c + 4 = -2.645751311 Simplifying c + 4 = -2.645751311 Reorder the terms: 4 + c = -2.645751311 Solving 4 + c = -2.645751311 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + c = -2.645751311 + -4 c = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 c = -6.645751311 Simplifying c = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. c = {-1.354248689, -6.645751311}Solution
c = {0, -1.354248689, -6.645751311}
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