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Simplifying 9 + 6c(2c + -1) = 0 Reorder the terms: 9 + 6c(-1 + 2c) = 0 9 + (-1 * 6c + 2c * 6c) = 0 9 + (-6c + 12c2) = 0 Solving 9 + -6c + 12c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -2c + 4c2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -2c + 4c2)' equal to zero and attempt to solve: Simplifying 3 + -2c + 4c2 = 0 Solving 3 + -2c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -0.5c + c2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.5c + -0.75 + c2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.5c + c2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.5c + c2 = 0 + -0.75 -0.5c + c2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.5c + c2 = -0.75 The c term is -0.5c. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5c + 0.0625 + c2 = -0.75 + 0.0625 Reorder the terms: 0.0625 + -0.5c + c2 = -0.75 + 0.0625 Combine like terms: -0.75 + 0.0625 = -0.6875 0.0625 + -0.5c + c2 = -0.6875 Factor a perfect square on the left side: (c + -0.25)(c + -0.25) = -0.6875 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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