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Simplifying 30 = 18c + -6c2 Solving 30 = 18c + -6c2 Solving for variable 'c'. Reorder the terms: 30 + -18c + 6c2 = 18c + -18c + -6c2 + 6c2 Combine like terms: 18c + -18c = 0 30 + -18c + 6c2 = 0 + -6c2 + 6c2 30 + -18c + 6c2 = -6c2 + 6c2 Combine like terms: -6c2 + 6c2 = 0 30 + -18c + 6c2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(5 + -3c + c2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + -3c + c2)' equal to zero and attempt to solve: Simplifying 5 + -3c + c2 = 0 Solving 5 + -3c + c2 = 0 Begin completing the square. 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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