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Simplifying -3c2 + 15c = 72 Reorder the terms: 15c + -3c2 = 72 Solving 15c + -3c2 = 72 Solving for variable 'c'. Reorder the terms: -72 + 15c + -3c2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + 15c + -3c2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + 5c + -1c2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + 5c + -1c2)' equal to zero and attempt to solve: Simplifying -24 + 5c + -1c2 = 0 Solving -24 + 5c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -5c + c2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -5c + -24 + c2 = 0 + -24 Reorder the terms: 24 + -24 + -5c + c2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -5c + c2 = 0 + -24 -5c + c2 = 0 + -24 Combine like terms: 0 + -24 = -24 -5c + c2 = -24 The c term is -5c. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5c + 6.25 + c2 = -24 + 6.25 Reorder the terms: 6.25 + -5c + c2 = -24 + 6.25 Combine like terms: -24 + 6.25 = -17.75 6.25 + -5c + c2 = -17.75 Factor a perfect square on the left side: (c + -2.5)(c + -2.5) = -17.75 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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