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Simplifying 6c(2c2 + -4) + -1c(8c) = 0 Reorder the terms: 6c(-4 + 2c2) + -1c(8c) = 0 (-4 * 6c + 2c2 * 6c) + -1c(8c) = 0 (-24c + 12c3) + -1c(8c) = 0 Remove parenthesis around (8c) -24c + 12c3 + -1c * 8c = 0 Reorder the terms for easier multiplication: -24c + 12c3 + -1 * 8c * c = 0 Multiply -1 * 8 -24c + 12c3 + -8c * c = 0 Multiply c * c -24c + 12c3 + -8c2 = 0 Reorder the terms: -24c + -8c2 + 12c3 = 0 Solving -24c + -8c2 + 12c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4c'. 4c(-6 + -2c + 3c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(-6 + -2c + 3c2)' equal to zero and attempt to solve: Simplifying -6 + -2c + 3c2 = 0 Solving -6 + -2c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -0.6666666667c + c2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.6666666667c + 2 + c2 = 0 + 2 Reorder the terms: -2 + 2 + -0.6666666667c + c2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.6666666667c + c2 = 0 + 2 -0.6666666667c + c2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.6666666667c + c2 = 2 The c term is -0.6666666667c. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667c + 0.1111111112 + c2 = 2 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667c + c2 = 2 + 0.1111111112 Combine like terms: 2 + 0.1111111112 = 2.1111111112 0.1111111112 + -0.6666666667c + c2 = 2.1111111112 Factor a perfect square on the left side: (c + -0.3333333334)(c + -0.3333333334) = 2.1111111112 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (c + -0.3333333334) equal to 1.452966315 and -1.452966315.Subproblem 1
c + -0.3333333334 = 1.452966315 Simplifying c + -0.3333333334 = 1.452966315 Reorder the terms: -0.3333333334 + c = 1.452966315 Solving -0.3333333334 + c = 1.452966315 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + c = 1.452966315 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + c = 1.452966315 + 0.3333333334 c = 1.452966315 + 0.3333333334 Combine like terms: 1.452966315 + 0.3333333334 = 1.7862996484 c = 1.7862996484 Simplifying c = 1.7862996484Subproblem 2
c + -0.3333333334 = -1.452966315 Simplifying c + -0.3333333334 = -1.452966315 Reorder the terms: -0.3333333334 + c = -1.452966315 Solving -0.3333333334 + c = -1.452966315 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + c = -1.452966315 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + c = -1.452966315 + 0.3333333334 c = -1.452966315 + 0.3333333334 Combine like terms: -1.452966315 + 0.3333333334 = -1.1196329816 c = -1.1196329816 Simplifying c = -1.1196329816Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.7862996484, -1.1196329816}Solution
c = {0, 1.7862996484, -1.1196329816}
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