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Simplifying 20c3 + 88c2 + -80c = 0 Reorder the terms: -80c + 88c2 + 20c3 = 0 Solving -80c + 88c2 + 20c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4c'. 4c(-20 + 22c + 5c2) = 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 '(-20 + 22c + 5c2)' equal to zero and attempt to solve: Simplifying -20 + 22c + 5c2 = 0 Solving -20 + 22c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 4.4c + c2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 4.4c + 4 + c2 = 0 + 4 Reorder the terms: -4 + 4 + 4.4c + c2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4.4c + c2 = 0 + 4 4.4c + c2 = 0 + 4 Combine like terms: 0 + 4 = 4 4.4c + c2 = 4 The c term is 4.4c. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4c + 4.84 + c2 = 4 + 4.84 Reorder the terms: 4.84 + 4.4c + c2 = 4 + 4.84 Combine like terms: 4 + 4.84 = 8.84 4.84 + 4.4c + c2 = 8.84 Factor a perfect square on the left side: (c + 2.2)(c + 2.2) = 8.84 Calculate the square root of the right side: 2.973213749 Break this problem into two subproblems by setting (c + 2.2) equal to 2.973213749 and -2.973213749.Subproblem 1
c + 2.2 = 2.973213749 Simplifying c + 2.2 = 2.973213749 Reorder the terms: 2.2 + c = 2.973213749 Solving 2.2 + c = 2.973213749 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + c = 2.973213749 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + c = 2.973213749 + -2.2 c = 2.973213749 + -2.2 Combine like terms: 2.973213749 + -2.2 = 0.773213749 c = 0.773213749 Simplifying c = 0.773213749Subproblem 2
c + 2.2 = -2.973213749 Simplifying c + 2.2 = -2.973213749 Reorder the terms: 2.2 + c = -2.973213749 Solving 2.2 + c = -2.973213749 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + c = -2.973213749 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + c = -2.973213749 + -2.2 c = -2.973213749 + -2.2 Combine like terms: -2.973213749 + -2.2 = -5.173213749 c = -5.173213749 Simplifying c = -5.173213749Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.773213749, -5.173213749}Solution
c = {0, 0.773213749, -5.173213749}
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