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Simplifying (4c + 3)(3c + 4) + 9(3c + 8) = 0 Reorder the terms: (3 + 4c)(3c + 4) + 9(3c + 8) = 0 Reorder the terms: (3 + 4c)(4 + 3c) + 9(3c + 8) = 0 Multiply (3 + 4c) * (4 + 3c) (3(4 + 3c) + 4c * (4 + 3c)) + 9(3c + 8) = 0 ((4 * 3 + 3c * 3) + 4c * (4 + 3c)) + 9(3c + 8) = 0 ((12 + 9c) + 4c * (4 + 3c)) + 9(3c + 8) = 0 (12 + 9c + (4 * 4c + 3c * 4c)) + 9(3c + 8) = 0 (12 + 9c + (16c + 12c2)) + 9(3c + 8) = 0 Combine like terms: 9c + 16c = 25c (12 + 25c + 12c2) + 9(3c + 8) = 0 Reorder the terms: 12 + 25c + 12c2 + 9(8 + 3c) = 0 12 + 25c + 12c2 + (8 * 9 + 3c * 9) = 0 12 + 25c + 12c2 + (72 + 27c) = 0 Reorder the terms: 12 + 72 + 25c + 27c + 12c2 = 0 Combine like terms: 12 + 72 = 84 84 + 25c + 27c + 12c2 = 0 Combine like terms: 25c + 27c = 52c 84 + 52c + 12c2 = 0 Solving 84 + 52c + 12c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4'. 4(21 + 13c + 3c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(21 + 13c + 3c2)' equal to zero and attempt to solve: Simplifying 21 + 13c + 3c2 = 0 Solving 21 + 13c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7 + 4.333333333c + c2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 4.333333333c + -7 + c2 = 0 + -7 Reorder the terms: 7 + -7 + 4.333333333c + c2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4.333333333c + c2 = 0 + -7 4.333333333c + c2 = 0 + -7 Combine like terms: 0 + -7 = -7 4.333333333c + c2 = -7 The c term is 4.333333333c. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333c + 4.694444446 + c2 = -7 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333c + c2 = -7 + 4.694444446 Combine like terms: -7 + 4.694444446 = -2.305555554 4.694444446 + 4.333333333c + c2 = -2.305555554 Factor a perfect square on the left side: (c + 2.166666667)(c + 2.166666667) = -2.305555554 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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