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Simplifying 2c3 + 6c2 + 56c = 0 Reorder the terms: 56c + 6c2 + 2c3 = 0 Solving 56c + 6c2 + 2c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2c'. 2c(28 + 3c + c2) = 0 Ignore the factor 2.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 '(28 + 3c + c2)' equal to zero and attempt to solve: Simplifying 28 + 3c + c2 = 0 Solving 28 + 3c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + 3c + -28 + c2 = 0 + -28 Reorder the terms: 28 + -28 + 3c + c2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + 3c + c2 = 0 + -28 3c + c2 = 0 + -28 Combine like terms: 0 + -28 = -28 3c + c2 = -28 The c term is 3c. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3c + 2.25 + c2 = -28 + 2.25 Reorder the terms: 2.25 + 3c + c2 = -28 + 2.25 Combine like terms: -28 + 2.25 = -25.75 2.25 + 3c + c2 = -25.75 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = -25.75 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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