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Simplifying 40c3 + -16c2 + 8c = 0 Reorder the terms: 8c + -16c2 + 40c3 = 0 Solving 8c + -16c2 + 40c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '8c'. 8c(1 + -2c + 5c2) = 0 Ignore the factor 8.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 '(1 + -2c + 5c2)' equal to zero and attempt to solve: Simplifying 1 + -2c + 5c2 = 0 Solving 1 + -2c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -0.4c + c2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -0.4c + -0.2 + c2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -0.4c + c2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -0.4c + c2 = 0 + -0.2 -0.4c + c2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -0.4c + c2 = -0.2 The c term is -0.4c. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4c + 0.04 + c2 = -0.2 + 0.04 Reorder the terms: 0.04 + -0.4c + c2 = -0.2 + 0.04 Combine like terms: -0.2 + 0.04 = -0.16 0.04 + -0.4c + c2 = -0.16 Factor a perfect square on the left side: (c + -0.2)(c + -0.2) = -0.16 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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