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Simplifying 3c2 + 30c = -105 Reorder the terms: 30c + 3c2 = -105 Solving 30c + 3c2 = -105 Solving for variable 'c'. Reorder the terms: 105 + 30c + 3c2 = -105 + 105 Combine like terms: -105 + 105 = 0 105 + 30c + 3c2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(35 + 10c + c2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(35 + 10c + c2)' equal to zero and attempt to solve: Simplifying 35 + 10c + c2 = 0 Solving 35 + 10c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 10c + -35 + c2 = 0 + -35 Reorder the terms: 35 + -35 + 10c + c2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 10c + c2 = 0 + -35 10c + c2 = 0 + -35 Combine like terms: 0 + -35 = -35 10c + c2 = -35 The c term is 10c. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10c + 25 + c2 = -35 + 25 Reorder the terms: 25 + 10c + c2 = -35 + 25 Combine like terms: -35 + 25 = -10 25 + 10c + c2 = -10 Factor a perfect square on the left side: (c + 5)(c + 5) = -10 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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