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Simplifying 2(4c2 + -1c) + -4(c + -2) = 0 Reorder the terms: 2(-1c + 4c2) + -4(c + -2) = 0 (-1c * 2 + 4c2 * 2) + -4(c + -2) = 0 (-2c + 8c2) + -4(c + -2) = 0 Reorder the terms: -2c + 8c2 + -4(-2 + c) = 0 -2c + 8c2 + (-2 * -4 + c * -4) = 0 -2c + 8c2 + (8 + -4c) = 0 Reorder the terms: 8 + -2c + -4c + 8c2 = 0 Combine like terms: -2c + -4c = -6c 8 + -6c + 8c2 = 0 Solving 8 + -6c + 8c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -3c + 4c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3c + 4c2)' equal to zero and attempt to solve: Simplifying 4 + -3c + 4c2 = 0 Solving 4 + -3c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -0.75c + c2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.75c + -1 + c2 = 0 + -1 Reorder the terms: 1 + -1 + -0.75c + c2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.75c + c2 = 0 + -1 -0.75c + c2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.75c + c2 = -1 The c term is -0.75c. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75c + 0.140625 + c2 = -1 + 0.140625 Reorder the terms: 0.140625 + -0.75c + c2 = -1 + 0.140625 Combine like terms: -1 + 0.140625 = -0.859375 0.140625 + -0.75c + c2 = -0.859375 Factor a perfect square on the left side: (c + -0.375)(c + -0.375) = -0.859375 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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