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Simplifying 10c7 + 30c6 + -50c5 = 0 Reorder the terms: -50c5 + 30c6 + 10c7 = 0 Solving -50c5 + 30c6 + 10c7 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '10c5'. 10c5(-5 + 3c + c2) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'c5' equal to zero and attempt to solve: Simplifying c5 = 0 Solving c5 = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5 + 3c + c2)' equal to zero and attempt to solve: Simplifying -5 + 3c + c2 = 0 Solving -5 + 3c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 3c + 5 + c2 = 0 + 5 Reorder the terms: -5 + 5 + 3c + c2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3c + c2 = 0 + 5 3c + c2 = 0 + 5 Combine like terms: 0 + 5 = 5 3c + c2 = 5 The c term is 3c. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3c + 2.25 + c2 = 5 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + 3c + c2 = 7.25 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (c + 1.5) equal to 2.692582404 and -2.692582404.Subproblem 1
c + 1.5 = 2.692582404 Simplifying c + 1.5 = 2.692582404 Reorder the terms: 1.5 + c = 2.692582404 Solving 1.5 + c = 2.692582404 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = 2.692582404 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 2.692582404 + -1.5 c = 2.692582404 + -1.5 Combine like terms: 2.692582404 + -1.5 = 1.192582404 c = 1.192582404 Simplifying c = 1.192582404Subproblem 2
c + 1.5 = -2.692582404 Simplifying c + 1.5 = -2.692582404 Reorder the terms: 1.5 + c = -2.692582404 Solving 1.5 + c = -2.692582404 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = -2.692582404 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -2.692582404 + -1.5 c = -2.692582404 + -1.5 Combine like terms: -2.692582404 + -1.5 = -4.192582404 c = -4.192582404 Simplifying c = -4.192582404Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.192582404, -4.192582404}Solution
c = {1.192582404, -4.192582404}
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