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Simplifying -4c3 + 16c2 + -28c = 0 Reorder the terms: -28c + 16c2 + -4c3 = 0 Solving -28c + 16c2 + -4c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4c'. 4c(-7 + 4c + -1c2) = 0 Ignore the factor 4.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 '(-7 + 4c + -1c2)' equal to zero and attempt to solve: Simplifying -7 + 4c + -1c2 = 0 Solving -7 + 4c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -4c + c2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -4c + -7 + c2 = 0 + -7 Reorder the terms: 7 + -7 + -4c + c2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4c + c2 = 0 + -7 -4c + c2 = 0 + -7 Combine like terms: 0 + -7 = -7 -4c + c2 = -7 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = -7 + 4 Reorder the terms: 4 + -4c + c2 = -7 + 4 Combine like terms: -7 + 4 = -3 4 + -4c + c2 = -3 Factor a perfect square on the left side: (c + -2)(c + -2) = -3 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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