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Simplifying 6c(3c + -1) = -42 Reorder the terms: 6c(-1 + 3c) = -42 (-1 * 6c + 3c * 6c) = -42 (-6c + 18c2) = -42 Solving -6c + 18c2 = -42 Solving for variable 'c'. Reorder the terms: 42 + -6c + 18c2 = -42 + 42 Combine like terms: -42 + 42 = 0 42 + -6c + 18c2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(7 + -1c + 3c2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + -1c + 3c2)' equal to zero and attempt to solve: Simplifying 7 + -1c + 3c2 = 0 Solving 7 + -1c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -0.3333333333c + c2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -0.3333333333c + -2.333333333 + c2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -0.3333333333c + c2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -0.3333333333c + c2 = 0 + -2.333333333 -0.3333333333c + c2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -0.3333333333c + c2 = -2.333333333 The c term is -0.3333333333c. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333c + 0.02777777779 + c2 = -2.333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333c + c2 = -2.333333333 + 0.02777777779 Combine like terms: -2.333333333 + 0.02777777779 = -2.30555555521 0.02777777779 + -0.3333333333c + c2 = -2.30555555521 Factor a perfect square on the left side: (c + -0.1666666667)(c + -0.1666666667) = -2.30555555521 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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