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Simplifying 5(2c + -2 + c2) = 5c + -15 Reorder the terms: 5(-2 + 2c + c2) = 5c + -15 (-2 * 5 + 2c * 5 + c2 * 5) = 5c + -15 (-10 + 10c + 5c2) = 5c + -15 Reorder the terms: -10 + 10c + 5c2 = -15 + 5c Solving -10 + 10c + 5c2 = -15 + 5c Solving for variable 'c'. Reorder the terms: -10 + 15 + 10c + -5c + 5c2 = -15 + 5c + 15 + -5c Combine like terms: -10 + 15 = 5 5 + 10c + -5c + 5c2 = -15 + 5c + 15 + -5c Combine like terms: 10c + -5c = 5c 5 + 5c + 5c2 = -15 + 5c + 15 + -5c Reorder the terms: 5 + 5c + 5c2 = -15 + 15 + 5c + -5c Combine like terms: -15 + 15 = 0 5 + 5c + 5c2 = 0 + 5c + -5c 5 + 5c + 5c2 = 5c + -5c Combine like terms: 5c + -5c = 0 5 + 5c + 5c2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + c + c2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + c + c2)' equal to zero and attempt to solve: Simplifying 1 + c + c2 = 0 Solving 1 + c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + c + -1 + c2 = 0 + -1 Reorder the terms: 1 + -1 + c + c2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + c + c2 = 0 + -1 c + c2 = 0 + -1 Combine like terms: 0 + -1 = -1 c + c2 = -1 The c term is c. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. c + 0.25 + c2 = -1 + 0.25 Reorder the terms: 0.25 + c + c2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + c + c2 = -0.75 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = -0.75 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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