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Simplifying 10c3 + -5c2 + -40c = 0 Reorder the terms: -40c + -5c2 + 10c3 = 0 Solving -40c + -5c2 + 10c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '5c'. 5c(-8 + -1c + 2c2) = 0 Ignore the factor 5.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 '(-8 + -1c + 2c2)' equal to zero and attempt to solve: Simplifying -8 + -1c + 2c2 = 0 Solving -8 + -1c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -0.5c + c2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.5c + 4 + c2 = 0 + 4 Reorder the terms: -4 + 4 + -0.5c + c2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.5c + c2 = 0 + 4 -0.5c + c2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.5c + c2 = 4 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 = 4 + 0.0625 Reorder the terms: 0.0625 + -0.5c + c2 = 4 + 0.0625 Combine like terms: 4 + 0.0625 = 4.0625 0.0625 + -0.5c + c2 = 4.0625 Factor a perfect square on the left side: (c + -0.25)(c + -0.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (c + -0.25) equal to 2.015564437 and -2.015564437.Subproblem 1
c + -0.25 = 2.015564437 Simplifying c + -0.25 = 2.015564437 Reorder the terms: -0.25 + c = 2.015564437 Solving -0.25 + c = 2.015564437 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + c = 2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + c = 2.015564437 + 0.25 c = 2.015564437 + 0.25 Combine like terms: 2.015564437 + 0.25 = 2.265564437 c = 2.265564437 Simplifying c = 2.265564437Subproblem 2
c + -0.25 = -2.015564437 Simplifying c + -0.25 = -2.015564437 Reorder the terms: -0.25 + c = -2.015564437 Solving -0.25 + c = -2.015564437 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + c = -2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + c = -2.015564437 + 0.25 c = -2.015564437 + 0.25 Combine like terms: -2.015564437 + 0.25 = -1.765564437 c = -1.765564437 Simplifying c = -1.765564437Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.265564437, -1.765564437}Solution
c = {0, 2.265564437, -1.765564437}
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