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Simplifying 8c3 + 11c2 + 3c + 3c = 0 Reorder the terms: 3c + 3c + 11c2 + 8c3 = 0 Combine like terms: 3c + 3c = 6c 6c + 11c2 + 8c3 = 0 Solving 6c + 11c2 + 8c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c'. c(6 + 11c + 8c2) = 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 '(6 + 11c + 8c2)' equal to zero and attempt to solve: Simplifying 6 + 11c + 8c2 = 0 Solving 6 + 11c + 8c2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.75 + 1.375c + c2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 1.375c + -0.75 + c2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 1.375c + c2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 1.375c + c2 = 0 + -0.75 1.375c + c2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 1.375c + c2 = -0.75 The c term is 1.375c. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375c + 0.47265625 + c2 = -0.75 + 0.47265625 Reorder the terms: 0.47265625 + 1.375c + c2 = -0.75 + 0.47265625 Combine like terms: -0.75 + 0.47265625 = -0.27734375 0.47265625 + 1.375c + c2 = -0.27734375 Factor a perfect square on the left side: (c + 0.6875)(c + 0.6875) = -0.27734375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
c = {0}
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