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Simplifying 4c = 2c2 + 8 Reorder the terms: 4c = 8 + 2c2 Solving 4c = 8 + 2c2 Solving for variable 'c'. Reorder the terms: -8 + 4c + -2c2 = 8 + 2c2 + -8 + -2c2 Reorder the terms: -8 + 4c + -2c2 = 8 + -8 + 2c2 + -2c2 Combine like terms: 8 + -8 = 0 -8 + 4c + -2c2 = 0 + 2c2 + -2c2 -8 + 4c + -2c2 = 2c2 + -2c2 Combine like terms: 2c2 + -2c2 = 0 -8 + 4c + -2c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 2c + -1c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 2c + -1c2)' equal to zero and attempt to solve: Simplifying -4 + 2c + -1c2 = 0 Solving -4 + 2c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -2c + c2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -2c + -4 + c2 = 0 + -4 Reorder the terms: 4 + -4 + -2c + c2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -2c + c2 = 0 + -4 -2c + c2 = 0 + -4 Combine like terms: 0 + -4 = -4 -2c + c2 = -4 The c term is -2c. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2c + 1 + c2 = -4 + 1 Reorder the terms: 1 + -2c + c2 = -4 + 1 Combine like terms: -4 + 1 = -3 1 + -2c + c2 = -3 Factor a perfect square on the left side: (c + -1)(c + -1) = -3 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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