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Simplifying c(c + 3) + -1c(c + -4c) = 9c + -16 Reorder the terms: c(3 + c) + -1c(c + -4c) = 9c + -16 (3 * c + c * c) + -1c(c + -4c) = 9c + -16 (3c + c2) + -1c(c + -4c) = 9c + -16 Combine like terms: c + -4c = -3c 3c + c2 + -1c(-3c) = 9c + -16 Remove parenthesis around (-3c) 3c + c2 + -1c * -3c = 9c + -16 Reorder the terms for easier multiplication: 3c + c2 + -1 * -3c * c = 9c + -16 Multiply -1 * -3 3c + c2 + 3c * c = 9c + -16 Multiply c * c 3c + c2 + 3c2 = 9c + -16 Combine like terms: c2 + 3c2 = 4c2 3c + 4c2 = 9c + -16 Reorder the terms: 3c + 4c2 = -16 + 9c Solving 3c + 4c2 = -16 + 9c Solving for variable 'c'. Reorder the terms: 16 + 3c + -9c + 4c2 = -16 + 9c + 16 + -9c Combine like terms: 3c + -9c = -6c 16 + -6c + 4c2 = -16 + 9c + 16 + -9c Reorder the terms: 16 + -6c + 4c2 = -16 + 16 + 9c + -9c Combine like terms: -16 + 16 = 0 16 + -6c + 4c2 = 0 + 9c + -9c 16 + -6c + 4c2 = 9c + -9c Combine like terms: 9c + -9c = 0 16 + -6c + 4c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -3c + 2c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -3c + 2c2)' equal to zero and attempt to solve: Simplifying 8 + -3c + 2c2 = 0 Solving 8 + -3c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -1.5c + c2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1.5c + -4 + c2 = 0 + -4 Reorder the terms: 4 + -4 + -1.5c + c2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1.5c + c2 = 0 + -4 -1.5c + c2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1.5c + c2 = -4 The c term is -1.5c. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5c + 0.5625 + c2 = -4 + 0.5625 Reorder the terms: 0.5625 + -1.5c + c2 = -4 + 0.5625 Combine like terms: -4 + 0.5625 = -3.4375 0.5625 + -1.5c + c2 = -3.4375 Factor a perfect square on the left side: (c + -0.75)(c + -0.75) = -3.4375 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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