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Simplifying -4c2 + 4c + -14 = 0 Reorder the terms: -14 + 4c + -4c2 = 0 Solving -14 + 4c + -4c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 2c + -2c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 2c + -2c2)' equal to zero and attempt to solve: Simplifying -7 + 2c + -2c2 = 0 Solving -7 + 2c + -2c2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3.5 + -1c + c2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -1c + -3.5 + c2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -1c + c2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -1c + c2 = 0 + -3.5 -1c + c2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -1c + c2 = -3.5 The c term is -1c. 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. -1c + 0.25 + c2 = -3.5 + 0.25 Reorder the terms: 0.25 + -1c + c2 = -3.5 + 0.25 Combine like terms: -3.5 + 0.25 = -3.25 0.25 + -1c + c2 = -3.25 Factor a perfect square on the left side: (c + -0.5)(c + -0.5) = -3.25 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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