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Simplifying (6 + -2c) * 3c + -3 = 27 Reorder the terms for easier multiplication: 3c(6 + -2c) + -3 = 27 (6 * 3c + -2c * 3c) + -3 = 27 (18c + -6c2) + -3 = 27 Reorder the terms: -3 + 18c + -6c2 = 27 Solving -3 + 18c + -6c2 = 27 Solving for variable 'c'. Reorder the terms: -3 + -27 + 18c + -6c2 = 27 + -27 Combine like terms: -3 + -27 = -30 -30 + 18c + -6c2 = 27 + -27 Combine like terms: 27 + -27 = 0 -30 + 18c + -6c2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + 3c + -1c2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + 3c + -1c2)' equal to zero and attempt to solve: Simplifying -5 + 3c + -1c2 = 0 Solving -5 + 3c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -3c + c2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -3c + -5 + c2 = 0 + -5 Reorder the terms: 5 + -5 + -3c + c2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3c + c2 = 0 + -5 -3c + c2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3c + c2 = -5 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 = -5 + 2.25 Reorder the terms: 2.25 + -3c + c2 = -5 + 2.25 Combine like terms: -5 + 2.25 = -2.75 2.25 + -3c + c2 = -2.75 Factor a perfect square on the left side: (c + -1.5)(c + -1.5) = -2.75 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. The solution to this equation could not be determined.
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