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Simplifying 4c2 + 72 = 24c Reorder the terms: 72 + 4c2 = 24c Solving 72 + 4c2 = 24c Solving for variable 'c'. Reorder the terms: 72 + -24c + 4c2 = 24c + -24c Combine like terms: 24c + -24c = 0 72 + -24c + 4c2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(18 + -6c + c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(18 + -6c + c2)' equal to zero and attempt to solve: Simplifying 18 + -6c + c2 = 0 Solving 18 + -6c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -6c + -18 + c2 = 0 + -18 Reorder the terms: 18 + -18 + -6c + c2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -6c + c2 = 0 + -18 -6c + c2 = 0 + -18 Combine like terms: 0 + -18 = -18 -6c + c2 = -18 The c term is -6c. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6c + 9 + c2 = -18 + 9 Reorder the terms: 9 + -6c + c2 = -18 + 9 Combine like terms: -18 + 9 = -9 9 + -6c + c2 = -9 Factor a perfect square on the left side: (c + -3)(c + -3) = -9 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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