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Simplifying 6c(c + 4) = 4c + -18 Reorder the terms: 6c(4 + c) = 4c + -18 (4 * 6c + c * 6c) = 4c + -18 (24c + 6c2) = 4c + -18 Reorder the terms: 24c + 6c2 = -18 + 4c Solving 24c + 6c2 = -18 + 4c Solving for variable 'c'. Reorder the terms: 18 + 24c + -4c + 6c2 = -18 + 4c + 18 + -4c Combine like terms: 24c + -4c = 20c 18 + 20c + 6c2 = -18 + 4c + 18 + -4c Reorder the terms: 18 + 20c + 6c2 = -18 + 18 + 4c + -4c Combine like terms: -18 + 18 = 0 18 + 20c + 6c2 = 0 + 4c + -4c 18 + 20c + 6c2 = 4c + -4c Combine like terms: 4c + -4c = 0 18 + 20c + 6c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 10c + 3c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 10c + 3c2)' equal to zero and attempt to solve: Simplifying 9 + 10c + 3c2 = 0 Solving 9 + 10c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + 3.333333333c + c2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.333333333c + -3 + c2 = 0 + -3 Reorder the terms: 3 + -3 + 3.333333333c + c2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.333333333c + c2 = 0 + -3 3.333333333c + c2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.333333333c + c2 = -3 The c term is 3.333333333c. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333c + 2.777777779 + c2 = -3 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333c + c2 = -3 + 2.777777779 Combine like terms: -3 + 2.777777779 = -0.222222221 2.777777779 + 3.333333333c + c2 = -0.222222221 Factor a perfect square on the left side: (c + 1.666666667)(c + 1.666666667) = -0.222222221 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. The solution to this equation could not be determined.
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