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Simplifying 2c = 32 + 8c2 Solving 2c = 32 + 8c2 Solving for variable 'c'. Reorder the terms: -32 + 2c + -8c2 = 32 + 8c2 + -32 + -8c2 Reorder the terms: -32 + 2c + -8c2 = 32 + -32 + 8c2 + -8c2 Combine like terms: 32 + -32 = 0 -32 + 2c + -8c2 = 0 + 8c2 + -8c2 -32 + 2c + -8c2 = 8c2 + -8c2 Combine like terms: 8c2 + -8c2 = 0 -32 + 2c + -8c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + c + -4c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + c + -4c2)' equal to zero and attempt to solve: Simplifying -16 + c + -4c2 = 0 Solving -16 + c + -4c2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 4 + -0.25c + c2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -0.25c + -4 + c2 = 0 + -4 Reorder the terms: 4 + -4 + -0.25c + c2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -0.25c + c2 = 0 + -4 -0.25c + c2 = 0 + -4 Combine like terms: 0 + -4 = -4 -0.25c + c2 = -4 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. -0.25c + 0.25 + c2 = -4 + 0.25 Reorder the terms: 0.25 + -0.25c + c2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -0.25c + c2 = -3.75 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = -3.75 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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